How does a real stopwatch work? Hint: it starts/stops on press, not release. So that's what the app should do, to map with prior expectations.

"Nobody uses real stopwatches anymore" might be somewhat true, but in athletics training they still do, and it just shows that it's not possible to adequately reproduce a thing on a touch screen and have it be as functional as the real item. A stopwatch app on a phone will always be a poor substitute for a real stopwatch.