OMG you do not need to do water changes every other day in a small tank. In my 2.5 gallon I do them once per week, about 1 third of the water to keep things fresh and stable. I do agree that it's just fine to do half the water as well. But maintaining the tank too often not only makes a pleasant hobby a chore, but also harasses the fish more than necessary.
The important thing is that you pay attention, and do more if you need to. Get a nitrate test - while nitrates are not the only concern, they are a great way to judge how quickly the conditions are declining.
They might be small tanks, but betta's are small, low-waste fish.
You have a filter, and that's the important part. The every other day advice is for people who keep them in cups or bowls, but then, that's just wrong in the first place.
Of course, sometimes people overfeed and then the tank gets dirty much faster. Feed just once per day, just a tiny bit (what he can eat in about a minute), and feed gradually so no food goes uneaten to rot in the water. You can even take a day or two off feeding every week, and if you go away for a trip, the healthiest option for the fish is to leave them without food.
