Reading this Reddit thread which tried to clarify this exact question, it seems that Haven won't reduce the damages of an AoE weapon like Evie's or Drogoz's:
Haven protects against all direct damage. Obvious things like kinessas rifle, victor rifle, Makao gun and hook, kinessa arrow, etc.
Blast Shield protects against any AOE damage at all. This includes direct hits from AOE shots and abilities. Drogoz rockets, Evie missiles, Pip flasks, even being stuck by Bomb Kings bombs.. this is all negated by blast shield. Haven will do nothing here. A few more things to consider worth mentioning: Victor grenade, Cassie's blast shot, Androxus's ult, and many others are also effected by Blast Shield.
Someone in this video also tested it with Evie and it shows that a direct hit is not reduced by Haven.
If you want an exact list of which capacities' damages can be reduced by Haven or Blast Shield, you can consult this picture, extracted from this thread: