I have the same issue. Rudder controls tiller is on, tiller is turning, nose wheel is turning.
However when I increase the throttle a little bit to get the aircraft going and I input full tiller to any direction, the aircraft seems to start turning in that direction but shortly after it turns to the completely opposite direction.
Regarding what srce said, I get the same red message that the gear is damaged when I pushback via GSX and I have the nose wheel lift option on. So this might be what causes the issue.
When I pushback with a towbar without nose lifting, the message doesn't appear and the airplane steers normally.
The workaround I see right now is to disable pushbackRaise option in GSX Menu > Customize Aircraft, however this setting is not persisted and will be turned back on every new flight.