MLB, welcome to the forum.
First, about SAE: they can get nippy but they are not belligerent and aggressive like CAE. But you will need to upgrade those SAE to at least a 20gal soon because they get about 6" long. Although your upgraded filter will take care of any water quality issues, the bottom line is the SAE will simply run out of room. Also, there is a possibility that what you have aren't the true Siamese Algae Eater but one of the many look-alikes. Take a close look at your SAE. The fins should be clear but the black bar that runs laterally along the body should extend into the tail fin. The scales should be clearly outlined.
This is a Flying Fox, commonly mistaken for a true SAE
This is a true Siamese Algae Eater
My guess is perhaps your SAE are nipping at your betta's tail. I've seen my SAE chase each other and sometimes go after the guppy that is in with them.