Ossification is a spell, but it doesn't target your creature (it targets the land it's going to enchant). It's ETB trigger is what targets your creature and that is what exiles, so there is no trigger event for your Rotpriest, since the creature is not targeted by a spell. It's very likely the same reason for the damage spell, but without knowing which card it was, it's hard to tell.

My rot priest did not trigger several times through my most recent fight.

I was ossified (ossification) by an opponent on my Fynn the Fangbearer while Rot priest was on the field, my opponent had no cards which would have prevented Rot Priest anywhere through out the field. Yet still he received no poison counter for targeting my Fynn.

This happened a second time with a damage spell that he cast against another of my creatures, both spells he used clearly said "target creature" and Rot Priest clearly states "whenever a creature you control becomes the target of a spell" I lost this match because of these poison counters not being applied several times. Please fix this bug.

Ossification is clearly a spell: "In MTG, a spell is any type of card cast by a player. Spells are usually cast from your hand, but in special cases can be cast from other areas of the battlefield like your library or your graveyard. Land cards are the only type of card that is not considered a spell." < from your own rules. These were all cast from his hand.

Note: it did work when I cast Tomito's Safe Keeping.

since you did not provide pictures I do not know what cards your opponent had on the field but there are some creatures that prevent triggered abilities from triggering. maybe the opponent had one of those and later it was dead