Almost. Depends how the drive or controller in question works. Not all are the same.
Normally:
1. If your drives are closed when there's no alarm condition then yes you would wire them in series.
There should be voltage running permanently through this circuit under normal condition.
When alarm opens one of them, the circuit is broken, voltage is dropped to 0v, controller then triggered.
2. If your drives are open when there's no alarm condition then you would wire them in parallel.
This time there should be 0v running permanently through this circuit under normal condition.
When alarm closes one of them, the circuit is made, voltage is applied, controller then triggered.
Joining of limit switches works in exactly the same way.
NC , Statement 1.
NO , Statement 2.
Not familiar with your controller type though. Are you using a breakout board or connecting direct?.
Directly. Your controller looks to be designed for NO switches. NO can't be wired in series.
Drives need ALM to be NO and parallel wired.
If drives are NO then pages 17-19 of your manual applies.
If drives are NC (or even limits are NC) I would use a breakout board with this controller so polarities can be swapped to suit each component with ease.