I paired my air pods to one of our apple TVs.  I took them out, put them in their case.  When I put them back on they went straight to the ATV.  (In my limited playing around... just got them yesterday... they connect back to the last device.  I have them paired to ATV, iPhone, iPad and iMac.)
So it appears I'll have to go to the settings to get it to connect to each device.  I didn't expect that.  Or I just haven't played around with them enough.