I have the same experience and always assumed it was caused by bowel contents putting pressure on the urethra in/around the prostate. I’d be interested to learn if there’s anything more to it than that and if it’s a uniquely male experience… (I assume you’re male?)

I believe this website explains it best.

https://motivatetherapy.com/2017/01/is-it-normal-to-pee-and-poo-at-the-same-time/

I’m pretty sure the muscles are controlled by the same nerves/neural pathways. A lot of people can’t shit without pissing also but once you have shat you don’t need to hold those muscles so you can let loose. It’s a bit like trying to wiggle your ring finger without moving your pinky or middle. Except with your dick.

I have always peed first and then defecated. It never occurred to me to try the reverse order.

The real question is can you shit and prevent yourself from peeing if you have a full tank.