Hi LittleCoffeeFox,
As you mentioned that it's happening while filming. It seems like an Auto White Balance issue. Are you using Auto White Balance on your cameras? Because usually, any slight change in the lighting may trigger Auto White Balance to compensate and cause such small changes in the color temperature. If this is what is happening you may want to lock the White Balance manually to have consistency between shots. Also, different cameras can meter light differently causing the exact same color temperature value to look slightly different. You may want to test these too for getting the best White Balance match between different cameras.
Thanks,
Sumeet