Yeah, it's definitely related to maturity and not season. Bananas can produce at any time of the year. Like Paulo said, the age to maturity/fruiting differs for various species. Proper mat maintenance can ensure more regular fruiting, but I don't know how well the 'planting 3 months apart' thing would work. I'm sure you could get fair results, but I doubt fruiting would necessarily coincide perfectly due to all the other conditions at play (weather, seasonal climate changes, fertilizer, soil quality, etc).
If you are serious about having a large number of plants for productive fruiting, I would contact Dr. Nelson about getting a copy of his DVD. Information about it can be found
in this thread. The video explains in great detail the methods used by commercial banana plantations to maximize yield and sustainability.