You have to make sure the transponder that comes with the rental car is disabled (the method varies) when you use your own transponder.
1. The rental transponder may have an on-off switch.
2. The rental transponder may slide in and out of a small box on the windshield (slide in to disable).
3. The rental transponder may need to be snapped off and stuffed in a special envelope (find that before taking off in the car).
4. You may need to explicitly decline the rental company toll paying option.
5. You may need to do more than one of the above actions.
Stick on (lite) transponders might not be transferable from one car to another; they may tear apart when you try to dismount them.
It is easy to forget and leave your own transponder in the rental car when you return the latter.
If you don't phone your transponder company and cancel the rental car license plate (if applicable) when you are done, you might continue to be charged, for the next renter.