"All tagging information is stored in extended attributes. This is similar to color labels and spotlight comments in Finder. Extended attributes are a feature of the Mac OS X file system (HFS).
Web URLs are treated special. They are stored in the Application Support and a copy of it in the Caches folder. This caches folder is being wiped by the cleaner app.
When you restart Tags the cache is being setup again".
I didn't find the above very helpful, and it didn't solve my problem of keeping track of websites I had tagged. Also looks like the data isn't in a database, but spread around all over the shop. Sounds like it might be worth making sure you're using HFS on your new macbook. Equally write to caseapps and see what they say.
Best of luck
Brian