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Do I have to ask for the CLI exactly when the 61 days pass or can i wait it out for a bit before i ask for it?
you can wait as long as you like.
You can apply for this "X3 CLI" AFTER the 61st day since your AMEX account was open. My AMEX BCE account was "opened" a few months ago on March 23. I did not apply for the X3 increase until June 9th, several weeks after my first eligible date! I was instantly approved and my CL was increased from $5K to my requested $12.5K. Yes, I "chickened-out" asking for $15k .. . !