I'm not completely sure but I believe I saw the +1 poison damage tack on in subsequent turns. Tough to remember now.
So if a unit has the trait 'Immune to "X"', does it really mean "X" can be applied to it, but it just won't suffer ill effects? Kind of like Mary can get infected with typhoid fever but it won't harm her? (BTW, don't ever eat anything Mary cooks.)
If I fight a monster that is immune to critical hits, can my character still roll a critical hit on him, have the critical damage and multipliers all get calculated out, only to have just the base damage actually get through then?
Seems like the least confusing approach would be to have 'Immune to "X"' mean "X" cannot be done against the unit in any fashion. In other words, I should not be able to poison a monster that is immune to poison.
If that's not what the designers intended, then I suggest considering changing the trait description from 'Immune to poison' to something like 'Takes no damage from poison'.