Should I just give all the rights on the copied files (db and apps) on the target server to the single oracle user ?
Correct, you need to change the ownership of the db/apps tier node files from the OS level to oracle user then run postclone on the database/application tier node as oracle user.
Remember, when one OS user you will need to source the correct env file each time you want to maintain a tier (i.e. source db env file for the database tier tasks/activities and source the apps env file for the application tier tasks/activities).
Perfect!Thanks a lot