If I set one of my devices to private listening, does that set all of them to private?

[denjanin]

I often control my music from one device and play through another - For example, if I turn a private session on my computer on, but I'm playing through my phone, does that still show up in peoples' feeds? I noticed that in order for it to say Private Session on my phone I have to switch it on separately. It would be nice if one switch on any devices just turned them all to private, if it's not that way already.