Check the metal plates that clamp the bottle necks.
Do they have 2 arcs cut into them? If so, pull the plates out and turn them 180 degrees.
Right now the plates are set on smaller circumference necks. You're breaking them because of that setting.
And yes, just push the levers down. If you apply too much downward pressure you can break off one of the handles.
The metal plates steady the bottle while the downward pressure of the bell crimps the caps.