Arabic term (edited): صرتِ تمونين عليه

I am giving this answer a "High" confidence level, not "Highest," not because I am not confident in my answer, but rather because the phrase itself is of unknown derivation and is used only in the colloquial language. Expressions of this kind typically do not have an ironclad definition. People feel free to use them in a fluid manner.

If I say, أمون عليك, that means that we have the kind of relationship that makes me expect you to be obliging to me in a way that I would not expect others to be. Perhaps you owe me favors, or we have suffered experiences together in a way that caused a bond to develop which makes you respond to my wishes obligingly, etc. So, if I ask you for a favor, I am sure you will oblige. If I give you advice, I expect you will give due weight to my advice. That is why people usually begin by saying, أنا أمون عليك, when they ask for a favor or when they counsel a friend.

When we say, أنت تمون علي, we usually mean to say, "how can I say no to you? I would do anything you ask."

Often people combine these two expressions. They say, أمون عليك وتمون علي, meaning we have a mutually obliging relationship. We have the kind of friendship that make us respond to each other without hesitation.

Therefore, صرت تمونين عليه كما تمونين علي essentially means that he has now become as obliging towards you as I am. He trusts you as I trust you, and he is willing to do stuff for you as you as you ask, just as I do.

Here is a link to an interesting article about this term:

http://alrai.com/article/541247.html

The article tries to propose an etymology for the term, but the proposal is speculative and cannot be ascertained. The proposed etymology seems to color the writer's understanding of the term and its origin. But the examples of usage given in the article make the common meaning pretty clear.