The TS431 looks pretty unstable in both sets of waveforms.
I haven't used the TL431 in regulators myself, but a few things don't look right.
Is C2 really meant to be across R3? I would think it would make the regulator overreact to transients which could cause those spikes.
Also the power mosfet driving circuit looks pretty weird to me. -15v in and -12v out - that means 3 volts across the gates of the N channel FETs. So even if the TLS431 is trying to turn the Fets hard off, the two FETS are still getting 3 volts in total across both their gates - so the TLS431 cannot turn the FETs hard off if they have minimum gate turn on voltages.
If the input voltage goes above 15V, I doubt there is any way the circuit could regulate. It is not a safe circuit.
It would be much easier to use a P Channel power FET (Drain and source swapped compared to the 5838 fet) with the gate going straight to the TLS431, and the IRF034 removed - and C2 removed as well. Now if the TLS431 is hard on, the FET will turn fully off.
The only catch is you need a bit more negative gate bias for the FET - 3v is probably not enough. If you are building the flyback supply powering this, there may be some tricks you can use to get a few more volts out to bias a P Channel Fet gate. For example, a capacitor from the 15V flyback transformer output (before the current diode) followed by a voltage doubler diode circuit using 1n914s would probably give you enough volts. You would definitely get over -15V.