When you say "primary sources" do you mean texts from our corpus of Latin and Greek or do you mean people who were contemporary with it? Classicists rarely use the term at all because of the fact that although most historians writing of various periods in antiquity are so far removed from us that they might be considered primary sources they are not actually contemporaries. We tend to just say texts.

Anyway, the most detailed accounts of Caesar's actual crossing are to be found in Plutarch and Suetonius, both of whom related the "alea iacta est" bit. Neither of them are contemporaries of Caesar's, however. Appian also describes the crossing in great detail, and Cassius Dio records it, though without all the nonsense that everyone else says--Cassius just says that Caesar crossed into Italy, without actually mentioning the river at all. Livy's 105th book supposedly detailed the beginning of the civil war, but it's been lost.

Of contemporaries we have pretty much nothing that mentions the river specifically. Caesar describes the beginning of the civil war in de Bello Civili, but omits any specific mention of the river, just saying that he marched troops into several Italian towns, which we know were on the opposite side of the river, though it is not mentioned. Cicero also does not mention the river specifically--like Caesar he just says that the army marched into Italy and seized Ariminum. The only way to get to Ariminum is either to physically cross the river or tediously go upstream until you're past it, which requires you to march a significantly longer distance and deal with the Apennines. Presumably it was clear to Caesar and Cicero that by marching into Ariminum you had to cross the Rubicon river. However, the importance of the river doesn't seem to have been terribly great during Caesar's lifetime, and certainly a sort of mythology got built up around Caesar's river crossing--to Caesar and Cicero what's important is that Caesar crossed over into Italy, out of his province of Cisalpine Gaul, and that he seized an Italian town (Ariminum). That fact alone is significantly more important than the crossing of a rather arbitrary boundary--indeed, though the Rubicon was legally the boundary of Italy, the enfranchisement of the Cispadanes meant that effectively the boundary was the Po, not the Rubicon, though of course proconsular armies could cross over the Po at will

Caesar himself wrote the first account of the crossing in Bellum Civile (The Civil War), though he spends far more time on the justifications behind it than the actual event (likely demurring on that subject because it was clearly illegal). In the lead up to it, Cicero also mentions the crossing's inevitability in a letter to M. Caelius Rufus (cclxxix).

It was not until later in the Roman era that the event was transformed into a mythical moment (alea iacta est).