Your description of a tree that blooms at night and flowers fall off in the morning sounds like Nyctanthes arbor-tristis: http://davesgarden.com/guides/pf/go/95610/ However, its flowers don't bear any resemblance to mimosa so maybe there's something else that also behaves that way.
Yes, ECRANE3, I looked. It's nothing like the flowers I saw. As I said, they had a diameter of about 8 inches, and were single, not in bunches. They looked just like mimosa, huge feathery things, spectacular! The leaves of the tree also looked like Mimosa.