Q: Managing Bluetooth devices

I have a pair of Bluetooth headphones that I like to use with my Mac, iPhone, and iPad. The problem I'm having is that requests to connect to the headphones seem to be ignored, and instead the headphones connect with the first device it can find,  and then hold onto that connection tenaciously. For example, if I want to use the headphones with my Mac, I have to go turn off the bluetooth on all my other devices so that the Mac can connect to the headphones successfully. And if THAT fails, I have to repair them.

I guess this is a question about Bluetooth technology in general, as opposed to an Apple issue, but I'm asking because of all the knowledgeable people here. Is this situation I'm encountering typical? Is it the responsible of the device (i.e. headphones) to manage its connections? Or are Bluetooth devices supposed to accept connection requests from known devices?

Any thoughts would be appreciated.