If you select a dino mid battle it’s not random, of course, so it sounds like you’re asking about the hit & run moves? And those will swap to the next dino in your lineup.
I have the following dinos pictured in this order on my screen:
Stegosaurus, Edmontosaurus, Sarcorixos, Triceritops
I open with a Stegosaurus. While stegosaurus is still alive, I swap to Edmontosaurus, causing the 75% swap in stun to be triggered. Edmontosaurus is now locked in for 2 moves (called binding, which occurs often when a swap in action is used). After two moves, I use hit and run with Edmontosaurus, triggering the next dino in order - sarcorixis, who immediately uses swap in shield.