Ron - Were you able to isolate where the water source was coming from.
I don't believe that the white power is mold I think that Scot has aim on what your seeing. Although the darker sections maybe supporting some dormant fungal activity especially if the woods moisture level is as your indicating dry 12% and below.

The water source may have had something in it that has left the white residue or crystals (salt?)

It appears very different than the plaster residue that we see on the subfloor framing on older homes.

Regards
Greg D. Dames
National ThermoGraphic Inspections
Pacific Mold Assessment