I am glad he's looking better now that you started the treatment with API fungus cure.
Among the causes of this disease may be high nitrite levels, rapid increase of water temperature, low oxygen etc. Is your tank cycled? You said it's a new fish... What about the tank? Is it also new? And it is small to be properly cycled... Maybe you should test your water. Also, it is very possible he got this disease while he was shipped.
Did you change the water on the third day? If not, do it today. Remove 50% of the water, then in the new water add 50% of API fungus cure dosage. Also, I would lower the water temperature to 76. This has to be done very slowly, not to stress the fish, no more than 1 degree/hour. One degree in a few hours would be even better. Decreasing water temperature will slow the growth of this bacteria. You can also increase aeration, as oxygen will provide conditions less suitable for it. If it possible to increase it and not bothering your betta, then do it, if not, keep it this way.
P.S. Don't forget to remove the activated carbon from filter during treatment.