Ugh, I struggled with this a lot when I was first learning to use a flash. What you're seeing is the intended design - in Av and Tv, the camera meters as if there was no flash at all. The idea is that it meters for ambient light (i.e. as if there is no flash at all) and then the flash output is responsible for the exposure on whatever the flash is lighting. The flash output is either set manually or via ETTL.
This threw me off because as a beginner, I would start with automatic settings, then turn to using manual ones one at a time as my comfort zone expanded. With flash, however, it's way easier to just go with manual - camera AND flash.
Look at it this way, with camera in Av and flash in ETTL, a slight difference in the shot, say a bit more sky in the frame, will change the shutter speed, unexpectedly altering the ambient exposure. And with ETTL, you're essentially telling your flash - go head - expose for what you think is right, I trust you! With that number of variables, it can be hard to just get a sequence of shots exposed consistently, much less have a properly controlled lighting situation.
So my advice is, start with camera in M. You can even use Av or Tv to first get the ambient exposure you want, then switch to M and dial those in. As you get more comfortable, you won't need that step - just start in M, set the shutter or aperture that you want, and dial the other one until the meter lines up. Now that your're in M, at least your ambient will stay the same and not be thrown off by metering. You can leave the flash in ETTL and use FEC to dial it in, but I wouldn't recommend it - I always found myself spending more time chimping and tweaking the FEC than getting the shot I want. So put the flash in M, take a few practice shots to find what it needs to be adjusted to, and voila - you have achieved a state of permanence. If the conditions, the distance/angle of flash to subject, etc stay the same, your shots will remain consistent and not be at the whim of automatic processes that can't possibly guess what exactly you want your shot to look like.
When I'm bouncing the flash or using some kind of diffuser, I'll use ETTL more often - it makes more sense in this scenario since, if you're moving around, the characteristics of the bounced light can change, and ETTL does a pretty good job of figuring out a decent exposure.
Disclaimer - there are a lot of ways to shoot with flash. My experience is based mostly on shooting people outside with off-camera flash. I chased what I believed was the ETTL holy grail that would do it all for me, buying the fancy PocketWizards, etc, but it seems that the more proficient I get, the more manual I get with my flashes...