Hi and welcome to Aquarium Advice!!
Bettamax does turn the water green. You don't need to use Bettamax all the time; like Endgame said, it's good to have on hand if your betta gets nipped by tankmates or gets finrot. Is he in a tank or bowl by himself? If he's by himself, you don't have to worry about nipping. Other causes for raggety fins are plastic plants. They can have sharp edges that can snag the betta's long, delicate fins. I have silk plants in with my betta.
How big is the tank or bowl? Spring water is ok, but I would still add some slime coat enhancement to the water. I use Novaqua (it's also a chlorine remover). I add 5 drops per gallon. The recommened dose is 10 drops per gallon, but I mix half tap water and half RO
water, so since the RO
water doesn't have chlorine, I half my dose of Novaqua. I've heard varying recommendations on the proper amount of Novaqua, from 5 to 10 drops per gallon (if you're using tap water), but you really can't overdose it, so I would say anywhere from 5 to 10 drops per gallon is fine.