It may depend on how long you held the mirror up there. The first time I saw Damien flare, it took a couple of minutes for him to figure out there was a problem. He just kinda looked at his reflection quizzicaly for a while, as though trying to figure out what in the world it was. Then, you could see it click in his little fishie brain that this might be an intruder, and off he went. He knows it's me putting the 'intruder' there, too. When I hold the mirror up to his tank, he'll flare at the reflection, then turn around and flare at me for a minute, then flare at the reflection again. It's like he's saying "Momma! Take him AWAY!!!!" It's really kinda funny.
I have two other bettas that are in a split tank next to one another. Sorensen, my feisty red crowntail will flare constantly at his tank mate. Luccien, my crown/plakat cross will just stare at him for a moment, then turn away as though Sorensen isn't worth his time. I think that infuriates Sorensen. I'm not sure which one is older, since I don't know Sorensen's age, but he acts like a put-out teen. The little brat... *snicker*
So, as you can see, it may depend on your betta's personality. Unless he's showing other signs of illness like lethargy and/or unusual color or growths, he's probably fine.