The AUR doesn't assume arch packages, if the package your aur script wants isn't in your repo then the package simply fails to update/install.

Edit: This is true even for Arch linux, as the Aur package might be out of date.

The problem is not the package. It is the packages Version. If you have for example an application that depends on .net 7.0 and arch updates it to the latest 8.0 then the AUR usually gets updated soon as well. Now the AUR pqckage depends on the newer 8.0 Version while manjaro still has the 7.0 version. The programm now does no longer start on manjaro.