I've watched the beginning of all 3 runs submitted for Derby Class and all 3 runs have started their timers at different times.

Redsplit started his timer after hitting Career in the menu nuu started his timer after Go! appeared on the screen of this first race arzim started his timer right when he loaded into the first race

It would be great if I could get some clarification on when the start time should be.

The run should should start when you select the first level, like in most racing games.