I understand that it's next attack only, took me a while to roll Silent Vow so I could test further but I found out what's happening.
The active "Sticky Slime" works 100% as intended but the "Slime Lord" ability that says you apply "Sticky Slime" when attacking does NOT cause them to attack you, I'm wondering if this is just a text error instead and it's suppose to only say "attacks apply slime" as opposed to "attacks apply sticky slime".
If this is just a text error then my bad I guess, if not and it's suppose to apply aggro you can easily test by equipping Silent Vow.
Screenshot of a battle with Silent Vow and 0 damage for reference.