If that's what it sounds like, it could very well be exactly what's happening. When you hit a bump, the suspension compresses, and then your wimpy stock shocks let it bounce back up. If the free length of your spring is too short, the suspension can easily extend beyond the length of the spring. Basically, you have more suspension travel on extension than you have spring length. Depending on how extreme it is and how you drive the car, this can simply cause some rattling and clunking, or it could cause the spring to dislodge from the spring perches in the worst case.

Jack up the rear of the car, put it on jack stands, and get under there. Are your rear springs loose in their perches? How loose?

Fixes can range from wrapping the ends of your springs with heater hose (might give you as much as 1/4" of additional length, but mainly will cushion the ends of the spring and eliminate minor rattles and clunks) to installing some sort of a "droop limiter" to keep the suspension from extending far enough to allow slack in the spring.

A droop limiter can be a piece of steel cable, a strap, or even a hefty zip tie. All it has to do is support the weight of the suspension when the car gets "light" over a bump and/or when the inside suspension unloads in a turn.

I'd start with some hose.

I'd also upgrade your shocks. Your stock shocks weren't designed to operate in the range that you're asking them to, or with the stiffer spring rates that you're asking them to.