Let's say for a minute I decided that I am going to use Aperture Priority (even though Manual would be better).
If I wanted to bring down the ambient exposure but not affect the flash exposure, would I just dial down EC? Or, would I have to dial up FEC to compensate for the dialed down EC too?
Here's something to keep in mind when using a flash - and you'll be able to solve ALL problems associated with using a flash - regardless of shooting mode!
Without a flash, we have the "exposure triangle" - F-stop, Shutter Speed and ISO. With flash you have added two more parameter - flash power and distance of flash to subject (not distance of camera to subject!) The amount of light thrown on subject decreases by the 1/R-square rule so your ambient background unless you are shooting in a 8x8 closet will NOT be lit by the flash. So, while your subjects exposure is affected by f-stop, flash power, flash distance, & ISO, your background ambient exposure will be controlled by the exposure triangle again - F-stop, Shutter Speed and ISO.
When you are on Aperture Priority and you dial in EC values you are telling your camera to change shutter or ISO to affect the overall exposure of the whole image - which includes the ambient background. If you change FEC, you are only telling the Flash to raise or lower it's output power to some value other than the calculated power based on data from the camera - and remembering that flash effectiveness has very limited distance, only your subject's exposure will be affect and the ambient background much less or not at all (unless you are in an 8x8 closet!!!)
Truth be known, I have never successfully shot with aperture priority with my D7100 or D90. I think Manual with the Nikon CLS system is the only way to go because basically with the CLS TTL you are really in aperture priority - you keep the shutter speed at highest sync speed of the flash, keep the ISO at lowest possible and start shooting with the desired aperture - aka "aperture priority" - the flash will do the rest for you. When it gives you the beep warning of not enough power, up the ISO by a stop etc.
I shoot exclusive with 2 speed lights (SB700s, both off camera in soft boxes) for all my events and model photography, indoors or out.
Hope this makes sense!