I've read that water/heat stressed trees will bloom out of season if they start to receive water and cooler weather. Is it possible the tree wasn't properly watered before you purchased it?

YES! That must be it! I had noticed that the trees seemed dry, and the lady at the store DID say that their water had been cut off for several days because of a suspected leak. That must be it. Thanks for shedding light on the mystery!

It's really not that uncommon for trees to bloom out of season. Another cause is disruption of the regular spring bloom and fruit-set. Apple, apricot, pear trees of all ages did that this year where I live, due to record cold in Feb and late spring frosts killing blossoms. I even saw some tiny pears begin to form in October!

I also saw some asian pears begin to form in late Sept. It was crazy this year. I once had an Anna apple bloom 4 times in one year in California. Just go with it, the tree will be fine.