Also, how can llblgen pro determine if it should still use DB1 for table X and DB1_customerone for table Y?
You can redirect references to databases or schemas by specifying name overwrites. If you need to access DB2, simply specify the name overwrite. Though that of course is valid for all references, so all DB1 references are redirected.
If you want to specify that per call, you can, in adapter. It's not that straight forward so I would definitely suggest to you to group the tables together in catalogs so they are threated like a unit: e.g. all tables shared for all customers in catalog A, and all customer specific tables in catalog B. You then can redirect per customer references to B to the specific customer catalog.
Please check: Using the generated code -> Adapter -> DataAccessAdapter functionality. You then can, per call, redirect references.