It's a process of learning, took me a lot of wasted feet of thin 32-36g wire to learn how to properly wrap an alien but I have a method that works 100% of the time.
Basically, tape up the cores about a quarter inch up the chuck end. Make sure they're nice and snug together in the tape. Then bend the 3 core wires evenly all at once with toothless pliers on the 1/4" section before the tape. Spread them into a triangle for each of the bends to fit into one part of the drill chuck & tighten it down on the tape, it'll spread them a little bit but don't worry about that.
Then what I do next once they're secured in the chuck is secure tension across the cores by running my index finger and thumb from the chuck to about half way up the cores pulling them straight. While you're holding it taught, put a piece of tape behind your index finger & thumb (like on the chuck side, not the swivel side) so they're secure.
Do the same thing but about 1" away from the end of the cores going into the swivel. Now, make sure everything is taught & laid flat horizontally from the chuck to the end of the wire. It's important that they're all parallel & horizontal going into the swivel. Bend them down 180° into the swivel (while holding tension on the cores) and pull the drill back to keep the tension.
Do a quick spin test to see if they're all staying completely flush & parallel and when wrapping, keep tension on the cores & wrap at all times.
That's pretty much how I align my 3 core 26g aliens, 28g&up I'll bend the cores into the swivel 180° & then over the cores again if that makes any sense.
If you have any questions, shoot me a message