That would be a proc proccing a proc. You need to apply the debuff yourself with an ability, like Backlash applying Minor Breach. To clarify: Trap applies Hemorrhaging, which applies Minor Mangle. Trap did not apply Minor Mangle directly, not like Backlash applies Minor Breach independently of whether it also applies Sundered.
ETA: same how Ele Sus does not proc EC - you apply the ability, the ability applies status effects, then the status effects apply the damage and minor debuffs, so all the elemental damage and minor debuffs are considered a proc and won’t apply Weaknesses from Elemental Catalyst.
Now proc sets can apply status effects (even when they don’t say they can), so procs do proc procs in that direction, but status effects won’t proc proc sets.