Domains don't necessarily have their own tapes.

Domains have policy sets.
Policy sets have management classes.
The management classes have backup copy groups.
The backup copy group points to a storage pool.

The storage pool may be disk or tape.
That's where the data goes.
So you can have all domains pointing at the same pools or different pools.

If you move a client to a different domain that DOES point the data to a
dedicated storage pool, it still only affects NEW data.  The already
backed-up data stays where it is.

Export/Import is the only way I can think of to actually move the data.