The podium doesn't move. Use the same little lever on the control ring that you'd used to make the piston connect, but push it sideways or up/down instead of diagonally. The ring will shift to give you a view of the next piston.

SOLVED - I actually worked with Cyan support (who were GREAT btw) and sent my save files and videos of the behavior of the piston couper control not repositioning - it turns out at that you can only reposition the coupler when the target piston is out of the frame of the reticle (viewfinder) of the coupler. Otherwise when you click and drag, the cursor does not move. If there's interest I will post a video. Hope this helps!