You want to be able to tuck both materials and have a strip that will lock the carpet and the tile.

If one is higher than the other you might want to use something like this with a snap-track.

That is the answer and the guy laying the tile should have helped with this since he was charging.

If you hired a pro, he's the flooring installer. It's his job to transition the flooring he just installed to the existing floor. That's you know......kind of the point of hiring someone to do an install for you.

When you start hiring "family friends" to do things, you get little details to finish up like this. Go get a transition strip like pictured by GN Builders, and if you don't want to worry about it next time hire someone you want a professional relationship with, not a personal one.