For that one it may be a combination of two things.
1. He starts out by asking if he can show them a magic trick. They say yes or nod yes. He then exits stage right. He then returns either through the back door or some the side stage left. Where he enters from is too far away from where he left for him to have walked or even ran there in the time between entrance and exit.
The part up to where he exists stage left could be pre-recorded. His wording and gestures change slightly with different people but he could have several different pre-recorded segments for this.
As Teller once observed:
> Sometimes magic is just someone spending more time on something than anyone else might reasonably expect
Penn has said something similar:
> The only secret of magic is that I’m willing to work harder on it than you think it’s worth
It could then switch to live for his return, where he then actually converses with them to prove that he's live.
2. If he encounters someone whose responses to the pre-recorded segment don't fit in, he skips them. Remember, we don't see how many people he had to try this with to get enough good ones for a video, and recall Teller's quote from above.
The one he's done that has me baffled is the one where he does this:
1. He asks them what city they live in.
2. He then tells them he used to live in that city and gives the address of where he lived. It is their address or an address of a close neighbor.
He also does this except instead of asking the city he tells them he has a talent for guessing people's names, and then tells them their name.
I can see in general how to do these, by using fake disconnects. He uses fake disconnects in one of his most common routines where he asks someone if he can show them a magic trick, starts a "pick a card" type routine, and then disconnects just has he's revealing their card. Then later when the person is connected to someone else either that someone else says "is this your card?" and holds up the correct card or he walks into that someone else's room and shows the card.
The key here is that he doesn't really disconnect. He just shows the disconnect screen, and then switches to feeding them video of the other person. They think that they have connected to someone new on Omegle but it is him the whole time.
With fake disconnects he could have his subjects in the "tell them their name" bit first talk to an accomplice who gets their name, fake disconnect and fake connect with him, and then he can do his name guess.
That should be fairly easy because people often exchange names on Omegle. But full addresses? I'd hope that would be rare, rare enough that even a Penn/Teller level of time would not be enough to get many people.