As per forums, to use space temple in "Supreme Commander 2" you need to click the teleport button and select the spot where you want your units to go, then select your units and right click the space temple.
The Space Temple Experimental Teleporter is an Illuminate major experimental unit. It creates a two-way teleportation conduit between it and any point on the map in its impressive range, which both allies and enemies can use.
According to IGN, your Airnomo likely didn't go with them, so send it in by itself. After they've all laid waste to the place, send a duo of Engineers across to build Mass Extractors, Shield Generators, and a small amount of anti-air turrets. To finish the job, ship everything—except the Airnomo, and one Engineer—back the way they came.
Since Supreme Commander 2's battles happen in real time, you'll have to think on your feet. Though the tutorial will prepare you for what's to come, there are many situations where you'll have to come up with your own solutions. Check out some tips to make things easier on you at IGN.