Brackish and saltwater food items are fine. The fishes do not contain too much salt just because they come from a high salt environment - rather they have developed ways of ridding their bodies of the excess. An example of that in crocodilians is the saltwater crocodile (also American croc). Both of these animals are more tolerant of the high salt conditions found in the sea and brackish waters than other crocs and gators are. The reason is that they have more well-developed glands (mostly on the tongue) that allow them to excrete the excess and maintain proper ratios of salt to water (osmoregulation). In addition, there are other things going on that help them regulate the salt content such as evaportative loss and excess intake via mouth and skin membranes. Even though they are more salt-tolerant, they will not drink saltwater, even if they are dehydrated. Actually, when all is said and done, salt to water ratios are pretty similar in all animals, regardless of their specific habitat.
There has been quite a bit of study and a lot of papers written about this. One source of easily understandable information is in the book “Crocodiles and Alligators” ed by Ross. In the section “Structure and Function” by Frank Mazzotti, an overview of this function is covered very well.
Probably more information than you were looking for, right?
Oh and by the way, mullet seems to be a fish that does not contain thaiminase (a bad thing) (see link) so you should be good to go. Just make sure this is not the only thing you feed it, they need a variety.
Thiaminase link
http://books.nap.edu/books/030903325X/html/64.html#pagetop
Bill
PS, living in a southern coastal town where mullet are found, I'm assuming you live in an area where there are indigenous populations of alligators. I trust you have the proper paperwork to keep them because they are Federally protected throughout their natural range.