Now, we really only need concern ourselves with the definitions that our sources use
.Arrian I 1 i
 ἅμα δὲ τῷ ἦρι ἐλαύνειν ἐπὶΘρᾴκης, ἐς Τριβαλλοὺς καὶ Ἰλλυριούς
However, at the approach of spring he marched towards Thrace, into the lands of the Triballians and Illyrian.
At the beginning of the spring he marched towards the Hellespont, entrusting the affairs of Macedonia and Greece to Antipater.
 ἅμα δὲ τῷ ἦρι ἀρχομένῳ ἐξελαύνει ἐφ᾽Ἑλλησπόντου τὰ μὲν κατὰ Μακεδονίαν τε καὶ τοὺς Ἕλληνας Ἀντιπάτρῳ ἐπιτρέψας,
III 6 i
Ἀλέξανδρος δὲ ἅμα τῷ ἦρι ὑποφαίνοντι ἐκ Μέμφιος ᾔει ἐπὶ Φοινίκης:
As soon as spring began to appear, he went from Memphis to Phoenicia,
IV 18 iv
 ἅμα δὲ τῷ ἦρι ὑποφαίνοντι προὐχώρει ὡς ἐπὶ τὴν ἐν τῇΣογδιανῇ πέτραν,
. At the first appearance of spring, he advanced towards the rock in Sogdiana,
 ἐκ Βάκτρων δὲ ἐξήκοντος ἤδη τοῦ ἦρος ἀναλαβὼν τὴν στρατιὰν προὐχώρει ὡς ἐπ᾽Ἰνδούς
As the spring was now over, he took the army and advanced from Bactra towards India,
Plutarch Alex.16 ii ‘Some, too, thought they ought to observe carefully the customary practice in regard to the month (in the month of Daesius the kings of Macedonia were not wont to take the field with an army). This objection Alexander removed by bidding them call the month a second Artemisius;’ combined with Arrian I 11 5, which tells us that it took twenty days to reach Sestos , it would appear that both Alexander and spring began in Artemisios 334BC which began 4th April.
For Diodoros there are no notices in Book XVII but two crucial one in XIX in chapters 45 ii and 50 i. Chapter fifty concerns the emerging pressure on the besieged in Pydna,
Chapter forty five deals with the contemporary flooding of Rhodes and allows us to define Diodoros’ usage in these passages;τοῦ δ᾽ ἔαρος ἀρχομένου καὶ τῆς ἐνδείας ἀεὶ μᾶλλον αὐξανομένης συνέδραμον πολλοὶ τῶν στρατιωτῶν καὶ τὴνὈλυμπιάδα παρεκάλουν αὐτοὺς ἀφεῖναι διὰ τὴν ἀπορίαν.
It is telling that exactly the same phrase is used in both passages as a chronological reference ἔαρος ἀρχομένου, the full story of the Rhodian flood gives the clues we need.ὁ δὲ τελευταῖος ἐπέπεσε μὲν ἔαρος ἀρχομένου, καταρραγέντων ἐξαίφνης μεγάλων ὄμβρωνκαὶ χαλάζης ἀπίστου τὸ μέγεθος:
So the flood occurred after the normal rainy season; the Mediterranean climate is generally assumed to be much like it was in Hellenistic times so when we look at the precipitation stats for Rhodes we find at this site http://www.holiday-weather.com/rhodes/averages/ a useful graphic which shows‘45 1 At this time occurred the third inundation of the city of Rhodes, which destroyed many of its inhabitants. Of these floods, the first did little damage to the population since the city was newly founded and therefore contained much open space; the second was greater and caused the death of more persons. 2 The last befell at the beginning of spring, great rain storms suddenly bursting forth with hail of incredible size. Indeed, hail-stones fell weighing a mina and sometimes more, so that many of the houses collapsed because of the weight, and no small number of the inhabitants were killed. 3 Since Rhodes is shaped like a theatre and since the streams of water were thus deflected chiefly into a single region, the lower parts of the city were straightway flooded; for, because it was thought that the rainy season of winter had passed, the drains had been neglected and the drainage openings through the city walls had become clogged. 4 The water that suddenly gathered filled the whole region about the Market and the Temple of Dionysus; and then, as the flood was already advancing to the Temple of Asclepius, all were struck with fear and began to follow various plans for gaining safety. 5 Some of them fled to ships, others ran to the theatre; certain of those overthrown by the calamity in their extremity climbed upon the highest altars and the bases of statues. 6 When the city and all its inhabitants were in danger of being utterly destroyed, relief of a sort came of itself; for, as the walls gave way over a long stretch, the water that had been confined poured out through this opening into the sea, and each man soon returned again to his former place. 7 It was to the advantage of those who were endangered that the flood came by day, for most of the people escaped in time from their houses to the higher parts of the city; and also that the houses were not constructed of sun-dried brick but of stone and that for this reason those who took refuge upon the roofs were safe. 8 Yet in this great disaster more than five hundred persons lost their lives, while some houses collapsed completely and others were badly shaken.
Such was the disaster which befell Rhodes.’
Oct: 60 mm, 5 days
Nov: 110 mm, 8 days
Dec: 140 mm, 13 days
Jan: 140 mm, 11 days
Feb: 130 mm, 10 days
March: 90 mm, 8 days
April: 30 mm, 6 days
May: 10 mm, 3 days
The most likely month for the surprise down pour would be April IMHO, synchronising this with the desperate straits at Pydna, so a much more precise reconstruction is actually possible, chronologically.
edited to change 'accurate' to 'precise in final sentence.