@Breebree567
I've not experienced that at all. In fact, I have an older Roku TV (TCL brand) that is so old and sluggish compared to the current sticks, that I have a Roku Stick plugged into it and use that instead. So, right there together are two Roku devices, both on, one streaming.
And, while watching the Stick-on-the-Roku-TV, I can watch on a Roku in another room.
All that to say I've not encountered what you're experiencing.
A question: when you say your Roku TV is "on" do you mean it's on but not streaming, or it's on and streaming. Those are not the same thing, after all, and the distinction may be important.
DBDukes
Roku Community Streaming Expert
Note: I am not a Roku employee.
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