How does an airplane do a Kulbit manoeuvre?
The Kulbit maneuver is a variation on the Cobra maneuver (Pugachev's Cobra) with a higher pitch rate and continuous positive pitch rate throughout the maneuver. It requires two things:


A docile pitch behavior of the airframe over the full angle of attack range of 360°. Docile means that the pitch moments stay low and do not change abruptly with the angle of attack.
Thrust vectoring nozzles to keep the pitch rate up.


An electronic flight system is helpful to make execution easier, but is not strictly required. Also helpful is an engine-intake-combination which does not stall the compressor if the outer flow is reversed briefly. As you can see, the control surfaces only play a minor role - they are only important initially to start the pitch-up motion. This is done by negative elevator and/or positive canard deflection.