I think a bare TL431 with a large smoothing capacitor, will be better than adding an LM358.
I've just done an LTSpice simulation showing the step response of the LM358 when the power supply voltage is changed from 9V to 12V and the output current from +2mA to -2mA and back again. Both scenarios generate pretty big transients on the output. I wouldn't trust the SPICE model though: do some bench tests.
The Spice models must not be exact, but I can hardly imagine a 100ns pulse edge in a system OP is elaborating (an another 358 generating some 150Hz sine I/Q stuff), however. LM358 itself is an 1MHz at unity gain opamp..
I don't know what power supply the OP is using, but a mechanical switch to change from 9V to 12V can create some surprisingly high frequency components. In real life I wouldn't expect a 100ns step response, but a bunch of pulses, as the switch bounces, with ringing causing some over and undershoot of the set supply voltage. The LM358's bandwidth makes its PSRR lower, at higher frequencies and therefore prone to interference when the power supply voltage is rapidly changed. I agree, about SPICE models not representing reality, hence my recommendation to bench test it.
Edit: regarding step response, the supply is very heavily decoupled so there isn’t a massive ramp up. I will test this on the bench.
How about when the power source is switched from 9V to 12V or will the never happen when the circuit is running?
What about a plain old 3.3V zener diode? It may not have so good regulation, but it will be faster than the TL431?
By the way, I don't have a problem with the TL431. I just think there are probably more efficient solutions.