Hard to figure out how a flush from the toilet upstairs would cause the bowl water here to move, unless there is a seal. (Well, I guess the porcelain being sealed against the floor could cause something of a vaccuum, but still...) And even with no wax ring whatsoever, if the toilet is properly-positioned above the closet bend, you shouldn't get much if any leakage -- the stuff should be shooting down the drain, with only a little splash or whatever leaking out.
That said, I would do the simple/cheap fix first. Pull it up. Put two rings on the floor (one without a plastic funnel on the bottom, and either another no-funnel ring above it or one with a funnel; never two with funnels; the funnel can help hold the upper ring in place. Alternative is a #10 extra-thick ring. Another alternative is the Sani-Seal. Put the toilet down carefully and vertically on top of the rings. Push straight down, smushing it down. You can feel the wax compress. It might smush a little through the holes for the closet bolts. That's fine. Don't shift it around because wax doesn't bounce back to fill gaps.
If this doesn't solve the problem, then if it is a two-piece I would check the tank-to-bowl connection for leaks; it could be that that water is dribbling down and around inside. Unlikely, but one rule of construction is that if you see water coming out somewhere, it often isn't a clear indication of where it's coming from. Water has a way of flowing around and out in unexpected places. (I traced water in a minimally-occupied condo structure once that was coming out the ceiling of the lobby. It started twenty floors up and way across the floor plate where a washer connection had been left flowing on the floor. [The story behind how that happened was classic.] The water went through undocumented slab penetrations, across walls, down the curtain wall, back onto floor, through other improperly-executed slab penetrations and ultimately out the lobby ceiling.)
After that, I would suspect a crack.
Let us know how it turns out.
