Abilities and Hidden Abilities are given separate slots. Unless you're playing across generation, these slots stay the same before and after evolution.
For your situation, if Eevee had its hidden ability, Anticipation, and then evolved into Espeon for example, it would keep the Hidden Ability slot and get Magic Bounce.
This same concept applies to all ability slots. If you had a Horsea with Swift Swim and evolve it into Seadra, its new ability would be Poison Point because the two abilities are in the same slot. Likewise, if said Horsea had Sniper or Damp instead, its new ability would be Sniper or Damp respectively upon evolution.
In my Eevee to Espeon example, where Espeon only has the main ability and hidden ability slot, both regular ability slots from Eevee are combined into one, but the hidden ability slot is untouched.
I hope this helps explain some of it. Source.