Does this not translate as "Mum is coming to buy my present"...?
It would be "Maman vient acheter mon cadeau", "venir de" + verb really shows that the action is very recent.
Mom is coming to buy = Maman vient acheter
Mom just bought = Maman vient d'acheter
As dorianbtdp said, venir de + Infinitif shows that the action was completed very recently.