I'm using a non hot shoe flash. By "exposure compensation" I mean I have to manually adjust exposure to compensate. I'm shooting fully manual.
In other words if I'm my meter says f11 at 1/160, ISO 200 when incident metering flash using my 5DIII and 135L, I have to shoot at F9, 1/160, ISO 200 for proper exposure. When I shoot with the same set up but metering using the over head tungsten light source my incident metering is spot on.
You've lost me now. I thought I understood from your clarification earlier what you were describing, but this new description suggests the exact opposite (i.e it's your flash shots that aren't metering correctly, rather than the ambient shots as you confirmed in post #6).
I don't think anyone's going to be able to explain what you're seeing until we know exactly which light sources are being metered, how the metering is being done (what mode the meter is in) and which sources are contributing to lighting the subject. Your latest comments make it sound as if you're metering only the ambient tungsten light, but taking a flash photo, which would only work if your flash wasn't actually illuminating your subject (at least not significantly relative to ambient), which would be a very unusual situation.
Can you isolate the problem to a flash metering problem or an ambient metering problem? Meter the ambient, shoot with ambient only. Then meter the flash (with overhead lights turned off, ideally) and shoot with only the flash. Which photo is correctly exposed?




