Some years I get around to lightly fertilizing my peonies (which are 10-15 years old), but other years I'm too busy and forget. I don't really see a difference--but that might be because they are really healthy already. On the other hand, peonies have been known to bloom for years at deserted farmyards and other abandoned places, so I guess they have some amazing survival traits.

My peonies only bloom a couple weeks also. However, some are earlier bloomers and others later bloomers. That might be what you were seeing in your neighbor's yard--earlier whites followed by some later whites.

Kate