How do egg incubators work?

You do not have to trek back to one building to do it. The Hatchinator in the outpost town is the named facility, but incubators also sit in your homeland base, at camp, and in the main city. An egg you pick up in the field can go into whichever one you reach first.

Where it goes does change one thing. Hatching runs on a timer, and visiting players can help accelerate hatch times inside another player's base. That makes your homeland base the incubator worth filling if you have people who drop in on you, and it makes visiting a friend's base something you can do for them rather than just a social call. A camp or city incubator gets no such help.

What comes out is a usable Aniimo, ready to go onto your team roster. An egg is a roster slot waiting on a clock.

Getting the eggs in the first place

Egg Heist is the mode built around them. You fight other players and try to extract with special eggs, so an egg is only yours once you have evacuated with it.

The central giant egg works differently. Whoever picks it up transforms into the egg and loses their combat abilities entirely, which means the carrier cannot fight back at all. The rest of the team has to escort them the whole way to evacuation. If you are the one carrying it, your job is movement and nothing else.

Not settled: How much a visiting player actually shaves off a hatch timer, and whether there is a cap on how often your base can be helped, is not settled.