how to deal with foreign keys with fixed values (on a db-table-basis)
The bottom line is that you can't define a foreign key constraint that uses anything other than just the columns in the primary key that you are referencing.

One of the ways that people sometimes use to consolidate keys across multiple tables is to use a GUID as the primary key.  If the tm_key in each of your tables was a GUID then you could impose the foreign key using declarative referential integrity without carrying the tm_db_tbl column in your some_client_table.

Failing that, your options are:


Forego declarative referential integrity and just ensure that you
have indexes that make your joins efficient. 
Impose referential integrity procedurally. 
Take ypercube's suggestion and find a more
efficient way to represent some_client_table.tb_db_tbl.