Ashen rune question/clarification

Part of the description of the Ashen rune states “A creature hit by an attack from an ashen weapon becomes surrounded by burning ash, which deals 1d4 persistent fire damage.”This has me thinking, does the ashen rune effect trigger on any attack action (shove, trip, etc.) you use with your weapon?

Of course your weapon would still need the necessary trait (or a feat specifying you’re using your weapon) for the attack actions.

Other damaging weapon runes like flaming and frost specify that their effects trigger on a successful strike. Runes like shock and wounding specify “on a hit”or “when you hit,” which can reasonably be extrapolated as ‘when you hit with a strike.’ The ashen rune explicitly says “hit by an attack,” the only other rune below level 10 to specify attacks in it’s description is the underwater rune, which negates the -2 penalty to attack actions while underwater.

I’m leaning towards it being: RAI the ashen rune only works on strikes but RAW it works on any attack action. I’m curious what you all have to say about it.

Thank you for reading and for chiming in!