as a quick note the way to tell when the reforms have taken place ingame ive noticed is to look at the town tab when youve selected a settlement. There should be a marker saying polybian era u can right click on or w/e. and i think most of the the time the barracks are actually replaced anyway but yeah it may be you have to upgrade.
If you want to see the requirements for reforms check:
https://forums.totalwar.org/vb/showthread.php?t=80502
hope that helps!