I know you don't choose a card until null time zone resolves, but when exactly does it resolve? If my opponent has initiative and plays null time zone during his recruit step, does he get to wait until my recruit step is over before choosing a card?

It resolves like this:

Player 1: Announces NTZ
Player 2 - Now has an opportunity to respond
Player 1: Announces the named card
Player 2 - Again, can respond, even with named card
Player 1: Can respond to your response, and if there was none, the effect has officially passed both players, and the chain is now empty, thus resolving.

I hope this answered your question.

Yeah, that what's I thought, thanks. I just want to make sure, the chain has to be empty before my recruit step officially starts, right?

Neither of those first two posts is actually how the card works.

First, the last effect on the chain resolves whenever both players pass on priority; this is just as true for Null Time Zone as it is for any other effect. You can only move on to the next step or phase by passing on an empty chain, so it's impossible for an effect to remain on the chain across steps. (As an aside, your opponent could wait to play Null Time Zone until your recruit step, if he really wanted.)

Second, because you only choose a card name during resolution, there is no more chance to sneak plot twists in at that point.

For every phase and step, every player must pass on an empty chain without adding new effects to move on. So an opponent playing NTZ at the start of the build phase, before the player with initiative gets his resource step, gets to pick the PT to lock before moving forward.

HC is correct; you may only play effects when you have priority to do so. During an effect's resolution, NOBODY has priority. Therefore, if you don't play plot twist X before the NTZ resolves, if X is named, you're out of luck for the rest of the turn.