The father is expected to fast on behalf of his underage (ie., younger than 13) son who is not obligated to fast himself. If his son is underage but old enough to fast (eg., 12 and a half, for the sake of argument), I think the point is that the father ought to attend the Siyyum with his son, in order to obviate the need to fast. The son does not have to fast at 12.5 years old any more than he has to fast at that age on any other fast day. For Hinuch it's probably a good idea, but it's not necessary.
As for technical Halachah, I assume - without sources handy - that the father is still the one responsible for either fasting or attending a Siyyum. However, since this part is Minhag (although there is an opinion that the head of household is included in the fast regardless of age of children or personal status as a Bechor or non-Bechor), it may not be a matter for technical Halachah.