Hi Rasmus,
It sounds, from your description, like you haven’t included the database in the migration operation. Make sure that you are uploading the database backup (the db.gz file), and ticking the checkbox to include it, when migrating.
I could be more sure about this if you could supply the exact version number of UpdraftPlus you have installed (which encodes information about the add-on status), and the migration log file. Though, I’m pretty sure, from the description you’ve given.
Best wishes,
David