Permissive to Tempered Parenting

Question for those seasoned nannies--

I am 36F working with a SAHM while the dad works full time.

Main kid needing assistance is 3 years 7 months and the younger child is a 10 month infant.

When I first started 3 months ago, the parents were painfully permissive. This is how they would speak to their child (who, at 3 years 4 months, still wears diaper):

"Can I change your diaper?" (Always was a no, followed by a fight)

"Where can I change your diaper?" (Always was a struggle. Kid would stand and refuse lay down, would kick during changing, etc)

"What do you want for lunch?"

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The kid having so much power would crumble when he didnt get his way, creating a very entitled and fussy personality.

For a while, the kid was super difficult with me - but learned that I was extremely no nonsense. I would be calm during arguments, and kept things very authoritative. I gave him 2 options, not endless choices, and encouraged creative thinking/problem solving instead of screaming for something he couldnt do (we cant do that, but what CAN we do? I gave examples a lot at the beginning and now he can do some himself).

It got to the point where although I was the strict one, he preferred to be around me and play/learn with me. I assum it is because he knew what to expect, and I didnt lose my cool like the permissive parents did.

I should add - this child is difficult, and the parenting is only a part of the puzzle. He's incredibly bright, and his parents make sure he knows it too (sometimes too much). But hes behind on so many things (still drinks out of a sippy cup - which I am training him out of. Doesn't know how to appropriately interact with other kids - which i try and help with by introducting park playdates. Often hits and rages when things dont go his way - which has stopped with me, but happens to his parents still)

More recently, the family has turned around entirely. If he doesnt behave one time, even minor, he immediately loses all toys (usually an empty threat, which confuses the kid even worse). He has been told he can go to Red Robin with daddy for lunch but when he doesnt listen to get shoes and jacket on quickly enough, he is abandoned by mom (that was one gnarly meltdown. I definitely felt awful for the kid on that day.)

My biggest concern is I am almost positive the kid is ADHD and most of his punishments come from not listening, which he needs assistance on (he listens decent with me but I am not where I want to be with him on it).

So, I am a first time nanny making $25/hr (ex web admin, government employee) - how should I approach this, if at all?

My idea has been "theyre not paying me to teach them how to parent, they are paying me to watch their kid" - and I will say, there has been a lot of positive change after they've watched my methods work, as much as Ive just stated things are difficult.

Would you talk to them?

My #1 concern is he will enter kindergarten incapable of connecting with other children and will also receive a lot of disciplinary actions. The parents dont want to send him to daycare, which I believe he desperately needs.

**sorry this is a jumbled mess and a ton of info all at once. Thank you all who took the time to read. It means a lot to me.