JD I'm not an expert by far but have not had any problems going from cup to container. What I do is this and I'm sure you will hear many other suggestions. Make sure your container is clean and has been sanitized if reused
Have your potting mix prepared and moistened a bit to hold form
When filling your new container place same size cup to where your little one will sit (height and center)
Fill around dummy cup and gently pack down a bit gently lift dummy cup and you should have a replicate hole
If root mass has been well formed as Jason has shown when you Tap it out of your cup it should be similar in size and shape as hole formed in pot and you won't be disturbing the roots much when transplanting Gently tap down and add any soil as needed for depth
Sal