15 gallons does not afford much room for many more fish = more waste.(possibly larger ,more frequent water changes).
Might add another 5 neons and call it good while keeping in mind that many tetra's enjoy much cooler water than betta's.
Many of the tetra species will live longer at temps not much above 76 degrees F, and most Betta's will appreciate 78 to 82 degrees F.
Many tetras also appreciate soft ,acidic water and aren't as flexible as some of the bettas in this regard .
Could /can be difference between fish that live a few week's,month's, and are frequently sickly,,or fishes that live two or three years or longer.
The most important medication in your fish medicine cabinet is.. Clean water.