This new AP article says that Snowden and his girlfriend vacated their home in Hawaii on May 1st. On its face that would seem to suggest that Snowden was on the job for now longer than the time between March 9th and May 1st. Of course, he could have left that home and remained in Hawaii for some period before leaving Hawaii and presumably ceasing his time on the job with Booz Allen. Snowden's own account is that he flew to Hong Kong on May 20th. That would still leave little more than two months on the job.
I should say there are other possibilities here. It's sometimes the case that someone in intelligence work will stay in what is in essence the same job but leave the government and go to work for a contractor. So possibly the alleged less than three months on the job with Booz Allen isn't the totality of his time in his last position. But something about this seems odd.
One more notable point: The AP story seems to somewhat bury the lede. It says that the real estate agent told the AP that "police came by on Wednesday to ask where the couple went. She told them she didn't know." We could allow the chance that police were asking about him because of some unrelated civilian issue. But that sounds more like a clue that authorities were on to Snowden before today.
If you take his story at face value he basically disappeared not long before a series of leaks began to emerge. If he really had the kind of access that he claims, presumably US authorities were already looking for him.