Mmmh if they are researching, probably you clicked on the icon to research the way to the mirror's world by mistake.
When you go in the battlefield tab, on the top right you can click on ''mirror'', it should show you how advanced in their research your squad is and if I remember well, you can cancel before the end and then either disband your squad or use it in the first world when their energy is up, as you wish.
The mirror's world as fewer people playing on it but you need to research the way to get there every time you get kicked out of the island. The ''research potential'' number in your pet tab next to their characteristics tells you how fast they will research in a squad when you'll try to go to the mirror's world. I recommend staying in the homeworld at first.