Does he only work on his ship or fleetwide?

All of the Fleet Commanders are Fleet Wide.

The wording of "Just that Ship" is generally "You".

Whereas, "Another Ship" or "A Friendly Ship" or something other than You , means it applies to someone else as well, at a minimum.

His actual wording:

"Before a friendly ship's Attack Step, it may choose to attack from only its left and right hull zones this round. If it does, it may add 2 red dice to its attack pool while attacking a ship."

Before a Friendly Ship

So as long as its a Friendly Ship, and its attacking an Enemy Ship, utilising only its Left and Right Hull Zones (since you can't attack Friendly Ships!) it Counts.

Just wanted an outside unbiased person to say so. Had an opponent saying it was just his ship. Much thanks.