Are "on hit" or "per hit" bonuses applied for skill hits, or just weapon hits?

Question

I have a per-hit bonus on my wand. Will this be applied every time one of my Prismatic Bolts strikes an enemy, or is it only for actual wand attacks? What about the "on hit" bonus on this helmet I have?

Answer 1

"On-hit" bonuses will only come into effect with a regular [Left Mouse Button] attack (only for actual wand attacks).

After experimenting on my good friend, Practice Dummy with Big Dog:

Here is my normal attack:

Here is my alt. attack:

As you can see, with the Alt. Attack, there is no +5 Health tooltip on my character, so they don't count towards "On-hit" bonuses.

This would be the same for "On-hit" bonuses on other items like helmets, etc.

Answer 2

Actually for some skills you do receive the on-hit bonuses from your weapon.

For example, the following berserker skills DO apply on-hit effects from your right hand weapon when used:
1. Eviscerate
2. Wolfstrike
3. Raze
4. Chain Snare
5. Ravage

These were all tested on the training dummy.