One thing I find useful when transplanting is to fill up the new container a little more than 3/4 of the way, dig out a little bit in the middle so your small container will fit, while judging how deep you want to plant.
Then take the small container and place it into the larger one and push dirt around it and then remove the small container, now you have a nice preformed hole to transplant into. Follow the directions above to get the plant out of the smaller container then set into the "preformed" hole you just created and gently back fill. Give a nice watering making sure you get both the new and old soil wet. This will further settle the new soil around the roots. After a couple of watering you may need to add more soil if it settles to much.
It has always worked good for me.