okay birds and bees time 
so fraternal twins are born when the chica has multiple eggs that month..it can be natural i.e. genetic or via fertility drugs usually make the lady have more than one eggs in that priod, a la octomom.
so all the man and his role is that the sperm go and fertilize 2 eggs ..or 8 as was the case of octomom.
so it is genetic for fraternal twins but since the man is not ovulating, his genes dont matter here.
so where do his genes matter, his daughters…so even if there is no twins on the mothers side, and lets say they have a daughter. This daughter can have fraternal twins.
next we have identical twins, where there is a single egg, and a single lucky sperm out of the many who make the trip…yaaay sperm..good job.
anyways, so something causes the fertilized egg to split, well its not an egg anymore but you get the idea. what determines that? now here there is no real proof and many scientists say that its random, however I think there is more to it because some families seem to have identical twins and some dont, I have 2 sets of identical twin cousins, second cousins, i.e. dad’s cousins kids, but then I also had idential twin older brothers atif and asif who sadly did not make it after a premature birth.
so my own view is that identical twins also run genetically and can be from mother or father, but I dont know enough or have not read enough about that.
sidebar…ever wonder why all these hollywood celebrities in their 40s seem to have twins recently? and its a boy girl set? ahhhh its IVF where they determine the gender of the introduced embryos before hand, nothing wrong with it in my view, but they claim it just happened…well must be something in hollywood water that you ladies who want twins should start drinking. anyhoo, no its not natural, its as natural as a blonde deis girl with roots showing claiming her hair colour is natural..like really no big deal if u dyed it, and you dont have to talk about it..but dunn lie n stuff.