The person controlling two characters may be using a program like DS4Windows or BetterJoy to convert their controller to Xbox, resulting in both the original controller and the converted Xbox controller being detected by Parsec. The person with the issue should look into their Parsec's gamepad settings, check if two controllers are listed, and press buttons with each one selected to check if they are the same controller.
If there is a duplicate controller, you can either close the program that is creating the second controller, or choose one of the controllers in Parsec's gamepad settings, then click Unmap on all of the buttons.
If there are no actual duplicate controller, then the host's game is likely the one causing this, in one way or another. If an emulator is being used, a common mistake is that the host has mapped multiple slots to the same controller, instead of each slot being assigned to a different controller.