Change between active/garrison is immediate (same turn, the change conceptually takes a little time, 1 month or so); you enter the Change Status action into your DO, alter the status in the army list at the same time, and start paying the new upkeep during that same turn. This should not be problematic.
Change to/from reserve takes a little longer (1 full turn, 3 months). Enter this into your DO, but don't change the status in the army list (the new status in effect at the end of the turn/start of the new turn), and thus no change in upkeep. The unit will be available for action on the following turn (either garrison or active, as you specified). That's how the rule is written and that's what the examples illustrate.
HOWEVER, with regards to the to/from reserve stuff; it might perhaps be easier to change that rule, so that you actually do change status on the turn you take the action (unit still won't be able to do anything) and thus change upkeep. The net result would be the same, but you'd save the money on the turn a unit goes into reserve and spend more on the turn its recalled to service.
Perhaps that option is both easier to track AND more conceptually sound? Any input?