Before answering, I'd like to clarify the exact definition of a reserve military force, which I'll use in my answer. A reserve military force is once which is composed of soldiers who undergo a training period, then return to their civilian lives, spending some amount of time each month or year staying brushed up on their military skills, so that in the event of war, they might be assembled into their units and sent into combat. While some reservists have prior active duty service, in most national reserve forces this isn't the case as far as I'm aware, and even in reserve forces like the US which often have ex-professional service soldiers and even hold themselves to a professional quality, many members do not have that active duty background.
Now, my Latin isn't the best, so correct me if I am wrong, but a phrase is idiomatic if it corresponds with something existent in Roman society, and is what a Roman likely would have called something. As such, let's ask what elements of the Roman military resembled our definition of reserve forces throughout its history.
The best comparison has to be with the pre-Marian Roman military, being composed as it was of citizen soldiers. This was, quite literally, an entirely reservist force. The length of time deployed for manipular legions does not necessarily mean that they could not have been considered "reservists," as modern reservists (I'm thinking of the US National Guard here) occasionally spend longer amounts of time deployed than regular troops. Here is where my flimsy Latin skills come into play. I'm not sure if there was an exact word for "citizen soldier," and a few preliminary searches aren't turning up anything. As such, I'll say that if the Romans had an explicit term for soldiers in the manipular army, those citizen soldiers, that would be the best idiomatic word for a modern Reservist.
However, if that isn't satisfactory, and you want an exact word, probably the best I can come up with is actually the noun "auxilia," or the adjective "auxiliaris." While this isn't the best word, it sort of works. It actually might be a better word for employees of PMCs, but the idea of "back-up" troops deployed to a combat zone to fill in the "gaps in the line" so to say, makes some sense, especially if you correlate modern reservists with, say, state volunteer Union army regiments from the American Civil War. The best argument in favor of "auxilia" is that the historical auxilia were, simply put, not professional troops, but rather were employed to supplement weaknesses in the professional Roman legions, and modern reservist units are primarily used to augment the professional forces of nations, especially those with rather small regular armies, such as Finland.