Comma placement with essential and non-essential clause

I was given two sentences and the task is to correct them or leave them the way they are. I’ve googled many examples and explanations of comma placement, but I’m still unsure whether my solutions are correct:

1. GIVEN:

• My parents used to tell me that if I crossed my eyes they would stay that way forever.

MY SOLUTION:

• My parents used to tell me that if I crossed my eyes, they would stay that way forever.

2. GIVEN:

• Now that I’m older and wiser I know that they were just making fun of me.

MY SOLUTION:

• Now that I’m older and wiser, I know that they were only making fun of me.

My question is: In the first given sentence, do I need the comma or not? Regarding the stuff I’ve read, I think I might not need that comma after all. In the second given sentence, I also placed the comma and I am more confident about that decision.

Thank you for the help 🙂