On Nikon (may be different to Canon), on my camera, the primary adjustment seems to be the ISO with iTTL but if I add exposure compensation, the flash increases and the ISO adjusts to meet the new requirements.

That said, I have found that different flashes in Nikon work differently (my SB600 vs SB700) as my SB700 cares which metering mode I am using and switches between BL-ITTL and ITTL while the SB600 doesn't so it could also come down to the flashes themselves for some of these issues.