My edges are wonky too, but that has more to do with me not putting down the fork than my sewing. Oh right, quilt edges, sorry.

On to your sewing problem.
It sounds like you put in a step that messed you up. If you are going to quilt the item. You don't really want to sew the edges together and then turn it out. There is no where for the "extra" to really go when you start squishing it around with the quilting process.
Try this experiment. Put something squishy like sugar cookie dough in a ziptop bag and smooth it out in a nice even layer. Drag your finger down the bag, leaving an indent. A small amount of dough is displaced by your finger, it has to go some where. It heads away from your finger and towards the edges of the bag. At some point there isn't anyplace else for the dough to go, and it starts to distort the shape of the bag or your finger design. If you had done the same thing with the dough between two sheets of plastic wrap, the sheets could shift and the dough could escape where it needed to. Then you could trim off the excess of both and make a neat "sandwich". The second method is the best option for items you are quilting. When you add the binding you will hide the raw edges of the quilt top, batting, & backing. You can get away with tying a quilt you have sewn and turned since there is more freedom of fabric movement with tying.

Good Luck!