Filling void under asphalt driveway
Possible causes: (not all of them equally likely)

Burrowing.
Poor compacting prior to paving.
Wood e.g roots, logs, garbage left under the gravel now decomposing.
Could be water erosion, perhaps a burst pipe.  That would probably be obvious though.

I'd make a small effort to determine what's causing it, but at this stage I wouldn't make too much effort at that, and jump quickly to exactly what you are planning to do.   If the situation returns I'd then dig it up and figure out what's causing it.
I wouldn't assume it's burrowing just because there is burrowing somewhere else.
It's a clue.  I have chipmunks, rabbits, groundhogs, voles, and hornets digging up my lawn constantly but I've never seen any of them burrow all the way under a paved driveway for no reason.   Might be a question of Outdoors SE.