The Pokemon that has pokerus in this case is a level 1 Deino, of some other OT, and the main topic of this question is a newly bred Horsea, level 1, and has never had Pokerus before. they were placed adjacent to each other. I battled something like 5-6 hordes and 9-10 Pokemon already, and Horsea simply won't catch pokerus.
Why is that?
PS - The Exp. Share was off, the time was 21:00, and I was not online, if any of that matters at all
Since your Pokerus Pokemon is in between a cured Pokemon (Talonflame) and a non-cured Pokemon (Horsea) the Pokerus' chance of spreading is cut in half. You are just extremely unlucky.
Try making Deino your second Pokemon with Horsea being your third and a non-cured Pokemon in the first slot. This should work.