That figures at 125lbs, which is more than enough for the system to come in to play. Likely the car sat lower until you started it, the air pump ran for a bit, the rear end picked up, and all was well. That is exactly how it is supposed to go.
The next move is up to you however. It might be best to go ahead and start a new thread so that we can hone in on what we feel the best solution might be for you. It may just be a case of new shocks, or maybe even a matter of raiding suspension pieces from something at the salvage yard.