Couple of things...
As a correction to the OP, this isn't a "flesh eating bacteria" like staph aureus (MRSA), it's a granuloma (lump) forming bacteria and it's infections are usually limited to the skin or the extremities like the fingers. It's pretty rare for the infection to spread to the bones or joints in otherwise healthy people (though this is a much bigger concern if you're immunocompromised (e.g., have HIV or are on chemotherapy or post transplant suppressants).
One of the biggest reasons that Mycobacterium marinum can cause serious problems is because infections are indolent (slow growing) so people wait too long before going to see their doctors, and it's pretty rare and so most physicians are somewhat unfamiliar with it and take a long time to correctly diagnose it.
In otherwise healthy people, infections can usually be treated pretty effectively with oral antibiotics so it's not something you have to worry too much about, but it's important to catch it as early as possible. If you do have a cut on your hand while working in a fish tank and you then notice swelling or a bump in the area it's important to go see your doctor sooner rather than later and tell him/her that you're worried about an M. marinum infection.
Not something to really worry about IMO, but as a fishkeeper it's important to be aware of this as a possible (though admittedly very rare) issue and learn to recognize possible symptoms.