Truck skates to the right on uneven surfaces

In my daily city driving, I occasionally notice on heavy bumps or dips that the rear end moves sideways as the rear suspension recovers from the road. A minor annoyance.
The other day I was traveling on a road under construction and got some air when I left the pavement that was about 6-8 inches above the gravel, at about 55 mph. Both surfaces were very flat, just a step down about 6 inches. Upon landing, the truck shifted violently to the right. I was going in an absolutely straight line when this happened.
Question: Why does the suspension seem to have this funny steering input from the rear when the suspension is compressed?
I have a 2011 Double Cab 4x4 with the OC (TRD Off-Road Extra Value Package) and TO (V6 Tow Package), with a dealer installed supercharger thrown in for good measure.

 

Check your tire pressure and set them all equal as a place to start. I assume that your tires are not the cheap Dunlops that Toyota puts on base model trucks like mine were. Second, I would physically examine your struts/shocks to ensure they are not leaking oil.

 

It's a byproduct of a solid axle and leaf springs. You get some rear steering input/bounce due to the suspension geometry changes during compression and rebound. I have had that effect on past Dodge, Chevy and Isuzu trucks. A 4-link or independant rear suspension would fix that...