Hi, yep, they do change colors! Would send a photo, please, so we can check? It's just that, red being a common color for many betta fish, it's probably just normal, but on the other hand, red is also the color of inflammation and disease on betta fish as on people and other animals.
Yes, I have a betta fish, who, when I brought him home, was originally blue and then slowly got darker and upon inspection with a flashlight, you could see that he was also turning more and more reddish in the dark red way autumn leaves change colors. He's fine and beautiful - that's just his adult color. He was about 8 months old when I got him - so now that he's about 3 years old - he's got his full, natural colors.