1.) "You" always refer to the ship an upgrade is equipped to.
2.) "Overlapping" refers to an object landing on another object (typically ship or obastacle).
3.) A ship's movement template is not that ship.
Result: The TIE/x7 gets a free Evade action after moving speed 3+, even if its movement template crosses and asteroid (or a debris if you can get rid of the stress in time). It only fails to get the free action if stress, or if it's base lands on another ship or an obstacle.
So PTL Defenders (Ryad) get to move across an asteroid, roll for damage, get a free action, and PTL off of that action to get another action.
Am I wrong here? I think I'm not, but I'm open to alternative arguments.