Traditionally, it was the audio front end equipment providing tone controls to the headphones. However, there is much ambiguity in equipment these days for things that should be standard protocol.
For example, my first Blu-Ray player. I wanted to send a secondary audio connection – optical or analog RCA – to a second input on my AVR that would allow me to have one input set up for audio playback, and another set up for movies. However, the player would not output audio via both HDMI and optical simultaneously. It was one or the other.
So, I made sure my next Blu-Ray player, a different brand, had dual HDMI outputs to accomplish the use I desired. Only to find out that it would output audio via HDMI and optical or analog RCA simultaneously. IOW, I didn’t need two HDMI outputs with that brand, and I could have used a cheaper player in their model line with a single HDMI output.
Thus, a function as simple as that, which should be universal across the product type (one way or the other), is instead a manufacturer-by-manufacturer thing. Even worse, you find no information in the user manuals answering the question for someone trying to do his research before he buys.
Likewise, there should be a universal standard in the soundbar segment as to whether or not a soundbar’s settings translate through to its various output connections. But I’m sure there isn’t.
All that to say, there’s no way anyone can predict if your soundbar’s modes or tone controls are going to show up in both its internal speakers and the headphones connected to it. You’re just going to have to take the plunge and “learn on the job,” as it were. Or find an on-line forum dedicated to the soundbar manufacturer’s products. Your chances of getting an answer here are slim, as our members in general aren’t fans of soundbars.
If the soundbar does send its audio processing to the headphone outputs, and the headphones have their own audio processing, you always have the option of using only one or the other.
Regards,
Wayne A. Pflughaupt