This a sign of aggression based on your description. Not
mating. Usually, this is a challenge put on by the younger betta and the older one is not phased by it.
Aggression in Bettas:
Male bettas are very clear about their aggresson, coming in forms of chasing, flaring, biting, and fin nipping.
Females are less obvious about it. They will 'square up' to their opponents and until one either starts the fight or swims away in a hurry, this will continue. They also flare and bite at their tank mates, especially if attacked.
What to do?
Provide the other people in the forum with the information they need (photos, videos, water parameters, and stock level).
Continue monitoring their behavior very closely. Bettas will
fight to the death.