No, the stick/flight control system doesn’t do anything upon ejection. The pilot will usually pull the nose up and get slow BEFORE ejecting if there’s no danger of the jet flying on too far and hitting somewhere/something with people, he wouldn’t want to do that in this case. Initial reports (can’t always be trusted) said that he was having hydraulic problems and ejected due to controllability problems. The seat going out pushes the nose down.
Pushes the nose in the opposite direction, anyway. I doubt it pushes hard enough to matter, much. What with the canopy blown off, and the speed that those rockets move the seat, I’m sure it’s a hell of a ride.