Welcome, and thanks for posting here in the Roku Community, @KN4248!
We appreciate you inquiring about this, and we'd like to provide the information you need.
The Roku Mobile App is specifically designed to connect to a single Roku device one at a time. Therefore, if you use the app to control one of your Roku devices, it will not mute or affect the audio on your second Roku, when trying to use the Headphones Mode on your other TV. Even if both Roku devices are linked to the same account, they operate independently.
We hope this clarifies everything. Let us know if you have more questions.
All the best,
Emman
Emmanuel-D.
Roku Community Moderator