The rules state:

"Any deaths also count towards your in-game time. Add the amount of time lost (time at death minus time when when you reappear)."

However, this is slightly ambiguous. In 16-bit Sonic 1 to 3&K (and probably CD too; haven't checked that), the on-screen timer keeps ticking for a few seconds after you die until the screen fades out and you reset to the last checkpoint.

So which time does "time at death" refer to? The moment when Sonic collides with the killing hazard and enters his death animation? Or the last time shown before the screen completely fades out?

So far I've been timing my runs using the latter, just to err on the side of caution.

As far as I know, it is the last frame where time is shown. For example: if you got hit and went to a death animation at 0:26, but the last number that was on the screen before it fades completely to black was 0:29, then 0:29 is what you subtract.