It is not possible to give a definitive answer to your question because there is no medically valid way to give a specific date or event that marks the onset of Alzheimer's Disease. The early stages of Alzheimer's Disease may be marked by changes in a person's mental condition and functioning such as forgetfulness of short-term details, increased difficulty in finding the correct word or problems in learning new information. None of these symptoms can be pinpointed to one particular event. Some of President Reagan's advisors felt he exhibited some of these kinds of behaviors while he was still in office as president, but they were not considered symptoms of Alzheimer's Disease at that time.
I have always wondered about this myself, and it would certainly explain Reagan's standard remark, "I do not recall," during his testimony concerning the Iran-contra affair. Reagan had used a similar answer, "I don't recall" when he gave testimony during a federal trial in 1962 concerning anti-trust violations while he was president of the Screen Actors Guild. (MCA and the SAG were charged; Reagan was not. The two organizations settled out-of-court and records were sealed.)
Obviously, Reagan could not have been suffering from the disease as early as 1962, but other people noticed a distinct change in his mental abilities while he was President.
Former CBS White House correspondent Lesley Stahl recalls an interview when he was president where "a vacant Reagan barely seemed to realize anyone else was in the room," and that before he "reemerged into alertness" she recalls that "I had come that close to reporting that Reagan was senile."
His memory was failing him while he was still President.
Once, while meeting with Japanese Prime Minister Yasuhiro Nakasone, he repeatedly referred to Vice President Bush as "Prime Minister Bush".
But, his White House doctors--all four of them--claim they saw no evidence of the disease while he was President. He first showed symptoms of the disease in 1992 or 1993, so it is possible that the disease had first taken hold during the latter stages of his Presidency, which ended in 1989.
There is no really good way to know for sure, but I would argue that Reagan did not actually have Alzheimer's while he was the president. His disease was not diagnosed until 1994, more than 5 years after he left office. More importantly, his doctors say that he did not have the disease during his time in office. People can speculate, of course, in the way that Reagan's son has. However, given that the doctors who were actually caring for him in those years say that he did not have it, there is no real reason to think that he did.