When CR00.7 talks about a player being given multiple extra turns, it's only talking about cases where a player is given those turns all at the same time, as with
Time Stretch and cards like it–it wouldn't make sense for a player to somehow take more than one turn simultaneously, so the rules specify that the turns are added (and therefore are taken) one at a time.
This case doesn't apply to your
Time Warp scenario, because the multiple different copies of
Time Warp are all resolving (and therefore giving their targets extra turns) at different times, not simultaneously.
So, what order do we take those turns in? Well, let's walk through the situation and find out. The active player plays Time Warp, but the nonactive player responds with Fork, creating their own copy of the spell with themselves as the target. No Time Warps have yet resolved, so no extra turns have yet been added, and we currently have only the normal turn structure–the active player's turns are color coded blue, and the nonactive player's turns are red:
AP (Current turn) -> NAP -> AP -> NAP…(And so on)
The copy of
Time Warp created by
Fork resolves and creates a turn for the nonactive player; we'll refer to it as T2, since that's what you called the Fork-Warp's extra turn above.
AP (Current turn) -> T2 -> NAP -> AP -> NAP…(And so on)
The original
Time Warp now resolves, creating a turn for the active player. As above, this will be T1.
AP (Current turn) -> T1 -> T2 -> NAP -> AP -> NAP…(And so on)
And finally, the active player plays a second
Time Warp, which then resolves and creates another extra turn for them (T3).
AP (Current turn) -> T3 -> T1 -> T2 -> NAP -> AP -> NAP…(And so on)
So this is the final order for taking the extra turns: T3, T1, T2, which is the reverse of the order those turns were created in