So - the solution: after pairing the Aeotec Siren 6 or Aeotec Doorbell 6, go to the advanced options and clear association groups 2 through 9. Always leave group 1 set to 1 though!
Note that when you clear association ID’s, that sometimes they appear cleared in the settings but are not actually cleared in the device. To fix that I often first put in a non-existing ID, save that, and then clear it again and save it again.