I've got a working theory here that if an ability (like brands's blaze) is applied by ability damage only then it will apply spell effects, whereas if it (like darius's hemmorhage) is applied by both ability damage and basic attacks, then it will not apply spell effects.
Again, this is a working theory, i'll keep checking it as more abilities come to mind, but it's checked out on the wiki with everything i've thought of so far.
EDIT: other abilities i've checked (note: i'm checking this on the wikia, not in-game so may not be correct)
Lux's Illumination applies only on abilites and applies spell effects (checks out)
Braum's Concussive Blows applies on both abilities and basic attacks, does not apply spell effects (checks out)
Leona's Sunilight abilites only, applies spell effects (checks out)
Vel'Koz's Organic Deconstruction applies on abilities only (although basic attacks refresh the duration of already-applied stacks), applies spell effects (checks out)
Ekko's Z-Drive Resonance applies on abilities and basic attacks, but applies spell effects (EXCEPTION - the way the wikia reads though, it sounds like the spell effects are produced on consuming the mark, not on application (Lux's Illumination by contrast reads like the spell effects are produced on applying the mark, which makes sense. One would assume that consuming illumination with a basic attack would NOT apply spell effects, but i could be wrong) so maybe not an exception after all? Needs more testing!)