IMO your tank is not big enough for any other fish and the CAE can get too big and soon its diet will change and it will stop eating algae all together and start sucking the slim coat off the Betta at night........
With any algae eating animal-they only eat some types of algae and will starve to death unless they are given supplement feeding-closed systems only offer limited amount of any one type of free range foods and rarely enough to sustain life long term.
I used to have a CAE in my 30 gallon, and I gave him extra food with what he was eating. He was very friendly and nice when he was little, but when he got older and more mature he turned pretty mean. he would suck on all my angelfish. I found him dead one day, I assume one of my bigger community fish killed him. but maybe you should place your CAE in a larger aquarium, for your Betta and for him. before mine died he was about 6 inches long..
I don't really understand why pet stores sell CAEs--it's terribly misleading to the customer to put a cute, innocent looking "algae eater" out on display, when in reality they get quite large and will eventually mature and its appetites will change from algae to the slime coat of your other aquarium inhabitants. A slow-moving fish like a betta has no chance. Return or rehome the CAE as soon as you can.