Congrats on AIP -- but sounds like DM to me!
You can pay it any time -- but by what you've said, I would pay it ASAP.
AIP is the eligibility stage. Just because you apply, doesn't mean you are eligible for the program you have applied under. The eligibility email is telling you that you meet the eligibility requirements to apply under that program. This is AIP. myCIC is note really something I watch anymore. ECAS is a better source of truth.
Log into ECAS:
https://services3.cic.gc.ca/ecas/authenticate.do Do so with your sponsor's details. This will give you access to see both sides of the application (there is technically 2 -- the sponsorship and PR application).
If that says Decision Made under both sides of the application, then you're done. It can take up to 10 weeks to get a landing date. This varies wildly based on your location (and the closest CIC office). Most are about 4-8 weeks. Etobicoke (GTA) and MTL are the longest waits.