Louisiana income tax for offshore workers

A blogger asked:

We just acquired a number of vessels that haul crude oil products along the Eastern coast line, Gulf, and Puerto Rico.  The vessels are dispatched out of Louisiana.  The employees live all over the place and where their residence  requires state withholding we are withholding that state income tax.

What I am  unsure of is:  when the employee lives in Texas,Tennessee or any other state  that does not require state income tax withholding, are we required to withhold Louisiana state income tax?

The general guidelines:

Louisiana considers that the waters within three miles of its coast are within the state of Louisiana, and this is the general standard to use when determining if Louisiana tax applies.