It does not. Melacula oil will help heal fins once the rot has been CURED, but will do nothing to make it go away. Tea tree oil is an antiseptic, not an antibiotic. Rot is caused by gram-negative bacteria, which needs meds that target that type of strain. Fin rot can also be treated with AQ salt.
Cajun, the bettafix (not melafix) is a super watered down version of melafix, so the dosing is around...errmm, I think 1/5 or 1/6. I use 1/4 of what I use for melafix, so as long as OP doesnt over do it, its ok :)
If hes sluggish, make sure he's in water thats between 76-81'F. Make sure your water is clean and conditioned. Do a water change of at least 50% right now for us.
To get rid of the rot, use aquarium salt at 1tsp/gallon of water. Pre-dissolve the salt outside of the tank and add in (it burns if not dissolved). Every day following, do a 100% water change and add new salt in. Do not compound the salt (ex, 1tsp.gallon one day, add another 1tsp/gallon the next)
Do so for no more than 10 days. He should be right as rain.