Actually, I'm not sure that the three months starts at the AIP. It may allow for the previous period of residence to be taken into consideration.
http://www.health.gov.on.ca/en/public/programs/ohip/ohipfaq_mn.aspx
Am I eligible for OHIP right away or do I have to wait?
There may be a three-month waiting period for your OHIP coverage.
Generally speaking, if you are a newcomer to Ontario, or a former resident returning here to live after being out of the country for more than seven months,
the waiting period begins on the date you establish or re-establish residence in Ontario. You may also be required to be present in Ontario for 153 days of the first 183 days immediately following the date residence is established in Ontario (you cannot be absent for more than 30 days during the first 6 months of residence).