You have the wrong adapter. You have a signal splitter rather an a dual mono to stereo converter. 3.5mm and 6.5mm jacks have multiple possible configurations of the connector. The most common are TS (tip/sleeve), TRS (tip/ring/sleeve) and TRRS (tip/ring/ring/sleeve). Each of these serves a different purpose.
In all cases, one portion is the ground, ...
If you're 'just' editing, at a push you can use pretty much anything.
If you're mixing, or any situation where you need to be aware of true EQ, levels or placement within a stereo field, then headphones can often be misleading.
With speakers, your brain can figure out not just what, but where each sound is & the relative levels between them. On ...
All Plantronics Bluetooth Headsets can pair with up to 4 different devices
Now the caveat seems to be that you can pair to 4 devices, but only connect to two devices and switch between them.
I guess you should call their support department and have a chat.