While there are some games that can set up autosplitters in various ways, most do indeed manually push a button for the times. In most cases, this will indeed not be accurate enough, so the actual time will usually be checked afterwards. For Super Mario Bros., there is a different way to calculate the time. The pattern Bowser has (Where he's moving and how he throws the hammers) is random reach time. This is changing for every frame from starting the game. So if you reach Bowser and hit the axe on the first possible frame, you can calculate the exact time it took based on the pattern.

Niftski actually got it on the 9th he just uploaded it hours later