Did you have the tyres changed recently? Sounds like someone messed up with fitting the valves or didn't fit the tyres properly and there leaking at the tyre beads. Like you say, kinda unlikely to have punctured them both.
Best way of knowing for sure is dumping them in a bathtub (with water obviously ) or something likewise to see where they're leaking.

There are more possibilities like you've bent or cracked both rear alloys on a curb/speedbump etc.