From my current understanding of the turn order, the start of a turn goes like this: Untap, Upkeep, Draw, all within the 'Beginning' of a turn (before the first Main Phase). During the Untap step, no player has priority, and it moves directly to the Upkeep step. This is when players first get priority, obviously starting with the player whose turn it currently is.
Here is the specific scenario I'm curious about:
Say I have a Krenko, Mob Boss on the field. I use his ability to create X tokens. Then, I play a Progenitor Mimic choosing Krenko. When the Legend Rule takes effect, I sacrifice the original Krenko. Since the Mimic comes in untapped, on my opponent's turn I tap it for the X tokens. My opponent takes and ends his turn.
Now it comes back to my turn. The Mimic untaps, and then copies itself during upkeep. Would I be able to tap the token copy after it's created for its X tokens, and then use the mimic later in the round for another X? Would the Legend Rule take effect before that could happen? Would I be able to tap the copy in response to the Legend Rule effect, placing the tap on top of the stack?