AndThe British scholar Nicholas Hammond made a thorough analysis of the probable dating of Alexander's birth in his "Sources for Alexander the Great" (Cambridge, 1993). Hammond shows that Plutarch probably got his date of 6th of the Attic month Hecatombaeon 356 B.C. for Alexander's birthday from a contemporary writer, Timaeus, who was also born in 356 B.C.
This is simply wrong as Plutarch cites Hegesias not Timaeus; and there is no given year for the birth of Timaeus, pseudo-Lucian 'Macrobioi' 22 says he lived 96 years and it seems his History ended in 264 BC (Polybios starts his History where Timaeus ended)but there is no year for either his birth or death But Hammond's claim needs examining.Basically, Cicero gives essentially the same story about Alexander's birth and the temple of Ephesus burning down as Plutarch does, and he too attributes it to Timaeus.
It is the emboldened passage that concerns us most but i give the whole chapter to set it in context. The first question we must ask is how much should be ascribed to Hegesias? Certainly verse six and probably seven but is there any reason to drag the statement about the date of Alexander’s birthday into the fragment? Once upon a time the trend was to try and allocate as much material to the primary source as possible, these days a much more conservative approach is adopted. On that approach the date would be excluded since it should be clear that the fact to which Hegesias’ frigid utterance is the burning of the temple of Artemis and not the foregoing matter. Those wishing to include the date would, presumably credit verses eight and nine as well. It is certainly not impossible but it is unrelated to the context Plutarch supplies for his Hegesian reference, towhit, the fire at Ephesos and so should be excluded.Plutarch Life of Alexander
3 However, after his vision, as we are told, Philip sent Chaeron of Megalopolis to Delphi, by whom an oracle was brought to him from Apollo, who bade him sacrifice to Ammon and hold that god in greatest reverence, 2 but told him he was to lose that one of his eyes which he had applied to the chink in the door when he espied the god, in the form of a serpent, sharing the couch of his wife. 3 Moreover, Olympias, as Eratosthenes says, when she sent Alexander forth upon his great expedition, told him, and him alone, the secret of his begetting, and bade him have purposes worthy of his birth. 4 Others, on the contrary, say that she repudiated the idea, and said: "Alexander must cease slandering me to Hera."
5 Be that as it may, Alexander was born early in the month Hecatombaeon, the Macedonian name for which is Loüs, on the sixth day of the month, and on this day the temple of Ephesian Artemis was burnt. 6 It was apropos of this that Hegesias the Magnesian made an utterance frigid enough to have extinguished that great conflagration. He said, namely, it was no wonder that the temple of Artemis was burned down, since the goddess was busy bringing Alexander into the world.7 But all the Magi who were then at Ephesus, looking upon the temple's disaster as a sign of further disaster, ran about beating their faces and crying aloud that woe and great calamity for Asia had that day been born. 8 To Philip, however, who had just taken Potidaea, there came three messages at the same time: the first that Parmenio had conquered the Illyrians in a great battle, the second that his race-horse had won a victory at the Olympic games, while a third announced the birth of Alexander. 9 These things delighted him, of course, and the seers raised his hopes still higher by declaring that the son whose birth coincided with three victories would be always victorious.
We must now examine the claim that this reference is actually from Timaeus, the foundation for which is a passage in Cicero’s ‘De Natura Deorum’, again I give the whole chapter for context,
One fact is immediately apparent; there is no mention of any date here but Cicero is clearly giving Timaeus the dubious credit for that lame remark plagiarism is cetainly a possibility but given the proximity of the two author’s floruits probably unlikely.DE NATURA DEORUM, II.
XXVII. Also, as the beginning and the end are the most important parts of all affairs, they held that Janus is the leader in a sacrifice, the name being derived from ire (' to go '), hence the names jani for archways and januae for the front doors
of secular buildings. Again, the name Vesta comes from the Greeks, for she is the goddess whom they call Hestia. Her power extends over altars and
hearths, and therefore all prayers and all sacrifices end with this goddess, because she is the guardian of the innermost things. Closely related to this function are the Penates or household gods, a name derived either from penus, which means a store of human food of any kind, or from the fact that they reside penitus, in the recesses of the house, owing to which they are also called penetrales by the poets. The name Apollo again is Greek ; they say that he is the sun, and Diana they identify with the moon ; the word sol being from solus, either because the sun ' alone ' of all the heavenly bodies is of that magnitude, or because when the sun rises all the stars are dimmed and it ‘ alone ' is visible ; while the name luna is derived from lucere ' to shine ' ; for it is the same word as Lumia, and therefore in our country Juno Lucina is invoked in childbirth, as is Diana in her manifestation as Lucifera (the Light-bringer) among the Greeks. She is also called Diana Omnivaga (wide-wandering), not from her hunting, but because she is counted one of the seven planets or ‘wanderers ' (vagari). She was called Diana because she made a sort of day in the night-time. She is invoked to assist at the birth of children, because the period of gestation is either occasionally seven, or more usually nine, lunar revolutions, and these are called menses (months), because they cover measured (mensa) spaces. Timaeus in his history with his usual aptness adds to his account of the burning of the temple of Diana of Ephesus on the night on which Alexander was born the remark that this need cause no surprise, since Diana was away from home, wishing to be present when Olympias was brought to bed. Venus was so named by our countrymen as the goddess who ' comes ' (venire) to all things ; her name is not derived from the word venustas (beauty) but rather venustas from it.
It is clear that Plutarch is writing from his notes, he mentions other sources naming Eratosthenes and noticing variant traditions. Cicero, on the other hand is interrupting an etymological waffle with an aside from the top of his head, the story not being germane to his thread. He is clearly muddled as his reason for calling on Diana during childbirth is ludicrous; it was her own labour-free birth that gave her a purview over births not the fact that pregnancy lasts a period of months! This need not mean that Cicero has mis-remembered, he would surely have spotted the error when he revised his draft before publication. The trouble is that it is generally thought that this was an unfinished work that had not proceeded beyond a first draft.
Further there would have been a good reason for Cicero to have Timaeus on his mind; during the summer of 45 BC (when ‘On the Nature of the Gods’ was being written cf ep ad Att. XIII

Given that Plutarch is writing specifically about Alexander and has his references, or at least his notes from those references, to hand how likely is it that the error is his? Any abbreviations of EGHSIAS and TIMAIOS are unlikely to have become confused. Whereas Cicero is writing the first draft of a work not concerned with Alexander at all and, it would seem, is dictating from the top of his head, certainly any sources he read in preparation were philosophical tracts, two of which he borrowed specifically for the purpose from Atticus. Is it not likely then that considering the sychronism of his work on Plato’s Timaeus he has had a lapsus memoriae which has remained due to the un-revised nature of the work.
So even if you insist on including the date data that should be firmly ascribed to Hegesias and not Timaeus whom Plutarch does not mention.