I recall that one of the positions within the legion was responsible for pay. A quick websearch turned up nothing. A slightly more exhaustive search turned up two different answers
Signifer: Each Centuria had a Signifer (59). He was responsible for the men's pay and savings, and the standard bearer for the Centurial Signum, a spear shaft decorated with medallions and often topped with an open hand to signify the oath of loyalty taken by the soldiers. It was this banner that the men from each individual Centuria would rally around. A soldier could also gain the position of Discentes signiferorum, or standard bearer in training. UNLV
Alternatively, Roman Empire.net identifies the aquilifer as the responsible officer.
The standard of a legion, the so-called aquila (eagle) was the very symbol of the unit's honour. The aquilifer who was the man who carried the standard was in rank almost as high as a centurion. It was this elevated and honourable position which also made him the soldiers' treasurer in charge of the pay chest. Roman Empire.net
The Roman Empire site specifies that they refer to the time of Augustus, which at the late end of your time period. Absent further research, I'd give them the nod for precision. Neither site is particularly replete with references.
In either case, each legion had someone responsible for the pay chest.