Chances are you are doing everything right...
You will see this behavior most often in the Schematic Editor. Here is a thread that may interest you that talks about what we refer to as 'servo bleed over'. https://decibel.ni.com/content/message/64512#64512
It is a bit of a bother when using the Schematic Editor to resolve servo postions (unplug ones you don't want moving if it is a critical issue).
Are you seeing the same behavior when you are in the middle of your driver controlled (teleop) operation, or just at the very beginning?
Is this a critical issue for your autonomy? If so, then make sure to initialize all the servos (we put the Move Servo call in a while loop that runs exaclty ONE time as soon as the program begins - this is allowed.) [how to do this is addressed in the thread linked to above]
You should find that even without a lot of effort the actual operation of servos during teleop and autonomy will resolve itself after that initial twitch.