Roman military presence in Judea

[LonginusXXI]

Was this Italian cohort an auxiliary unit? If so why would Italians join the auxiliaries and not a legion? Are they many examples of this?

No. It was a unit of citizen volunteers raised by Augustus.

According to this post:

“One should keep in mind that there's a difference between 'normal' auxiliary units that received the title CR as an award for extraordinary service and units raised from Roman citizens (i.e. the earliest cohortes Classicae, the cohortes civium romanorum voluntariorum, etc). 
As Caius said, the former kept that name as a reminder of the honor. They may have recruited citizens from then on, but I'm not sure there's sufficient evidence to prove that. On the other hand, throughout the second century, there would've been more and more citizens in auxiliary units (sons of former auxiliary soldiers), simply because the system produced such potential recruits.
Of the original cohorts of Roman citizens some date, I believe, from the later Augustan era, around the Pannonian revolt of 6 AD. It is indeed possible that Augustus did not want to raise another - permanent - legion for a crisis situation. That would not only require even more highly paid citizen troops (cost of soldiers was very much a factor in his politics!), but it was also another potential security risk for which a dependable senator needed to be found.”