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Here is what I found after my testing. Since I do not have soft box, I could not test soft box color shift.
I set my WB as flash for all this test to start with, picture are taken in Raw mode, imported into light room 4. No other setting/adjustment ware done, other then adjust WB as auto in light room, here are my finding.
Einstein kept about 8 foot in constant color mode for various power level.
Here are WB values displayed in light room after changing to auto from flash mode
Bare bulb - Color temp:5100 tint:0
Bare bulb with expo disc - 5500 tint:+5
8.5 inch high output reflector - 5300, tint 0
8.5 inch high out reflector with expo disc - 5650, tint - +7
Shot through umbrella - 6050, tint -0
Shot through umbrella with expo disc - 5700, tint -0
reflective umbrella - 6100, tint - 0
reflective umbrella with expo disc - 6050, tint -0
PLM with silver umbrella - 5500, tint -0
PLM with silver umbrella with expo disc - 5550, tint -0