You can use video editors to retime runs to start at the same frame as well as end at the same frame. Don't know how usual that is on most games, but that's what I do on Outlast any%, although I only have timed WR runs, not gonna bother with every run.

Usually people don't care enough to get an accurate time beyond the seconds.

If they do (For example a tied WR?) then the runs can always be retimed, so there isn't really a problem.

Beyond those points, as well, there's generally no other way to do it, particularly with consoles. Some autosplitters are available for some PC games but for the vast majority of games, it'll take some time to do any splitting automatically.

Generally speaking when starting a timer you just be doing so just before the first real input and end it after the last input, like mentioned before once you need to actually time it to the millisecond which most don't since its fairly uncommon to need, you can always re-time from the starting frame to the last frame of the run. Most else its just getting it down as a practice so you get better at it manually which is how 90% of runs are done anyways, splits in-between are not very important unless your looking to improve certain segments of the games you plan to run. Practice practice practice. Most times splits are done at the earliest and most convenient times in the runs like load screens where you cannot give any input thus allowing a few secs to manually place the split, keep in mind tho the overall time is what really matters for runs unless you plan to improve certain parts of the run.