If the ambient light is such that your subject is nicely, evenly lit, you need not bother with fill.
If, however, your ambient light leaves shadows that are too dark, you can use fill flash to fill them.
In most cases, those dark shadows occur because the main light source is either behind or beside or above your subject. You fill in the shadows with flash that originates closer to the camera.
Usually you don't have to worry much about the fill flash and the ambient light adding together, resulting in over-exposure, because the direction of the two light sources is so different. If the direction is similar, you can consider adjusting your settings to take the additive nature of the light into account.
So normally you set things opposite from what you said in your post - your ambient light exposure is normal, and the fill flash is less, because it is okay that the shadows appear as shadows, as long as they are sufficiently light as to record the detail and texture you want. Some like darker shadows, others like lighter shadows. I tend to prefer shadows that are illuminated by one stop of light less than "normal" (or underexposed by one stop).
This is all oriented toward fill flash. There is nothing stopping you from making the flash the main light, and letting the portions of the subject lit by ambient light be underexposed by one stop.