I think people give the cue of stopping urination to help others find the muscles that you need to engage. Otherwise, yes, you absolutely can just do them any time you want. In yoga it’s called mula bandha [1]. You’re often instructed to engage it while practicing asana or pranayama. I even focus on engaging it when I’m out for a run or lifting weights.
[1] https://en.m.wikipedia.org/wiki/Bandha_(yoga)#Mula_bandha