I had this problem with my four cameras. You do not say whether your cameras are wireless or hard wired. Wireless are prone to interference than hard wired. . .although they are not totally immune to the problem you have.
When you are not running your engine you are drawing power from the battery which is clean DC.
When you run your engine, you are charging the battery from the alternator which puts out a bit higher than the battery voltage and a bit "dirtier". Installing a filter that feeds the camera can (sometimes) cure this.
If it doesn't, check the voltage to cameras (with engine running) to see if you are getting 12.7V. It should be no higher.
These made in China goodies are mostly designed for surveillance videos and work great with power supplies with stellar filtering systems.