This is in essence just restating what others have posted.
The flash meter used in incident mode measures the light output from the flash at the subject's position.
If you have the flash set to auto, the auto function will vary the light output according to how much of the light output bounces back to the sensor on the flash. This depends on distance and, among other things, what the reflectance is of the subject and its background. Depending on how you set things up, the presence of the flash meter itself in the scene may affect how much light bounces back to the sensor.
If your subject and the surrounding scene happens to average out to a reflectance of 18%, your meter will indicate the same setting as the auto aperture set on the flash (assuming everything is properly calibrated). In the real, non 18% world, the meter will indicate something different.
If you are going to use a flash meter, you need to use the flash on manual.