The timer for Spelunky Challenges is paused between games. Depending on the games included time should be counted as follows (unless specified otherwise in the category itself):

• Start Classic on first frame of a level being shown. End Classic on first frame of ending cutscene
• Start HD on last frame before player movement on a level. End HD on first non-black frame of ending cutscene
• Start S2 on last frame before player movement on a level. End S2 on first non-black frame of ending cutscene

The Triathlon Calculator can help simplify timing your runs.