I would love to hear some string teachers address their sequences for vibrato. My own (still evolving) is...

1) Polishing the string
2) Polishing the string while the thumb stays in place
3) Slowly applying pressure until the left hand finger is rolling instead of sliding
4) Practicing at different speeds with a metronome.

Step 2 is a big one for students to make and takes a lot of individual instruction to keep the wrist from flexing. Is there an extra step that would make my students more successful?

Vibrato can be hard. Check out this book, Playing The String Game by Phyllis Young. She has some great suggestions on fun games to play to get your students on the right track.

I tell all my students that they need a few prerequisites regarding how they hold their instrument before vibrato will work at all.

With vibrato, there are 3 points of contact from the instrument to the body.

1. Thumb to neck of instrument (thumb MUST be loose and not "grasping" the instrument)
2. The finger being vibrated (this finger must be tall, and only the tip of finger on the instrument)
3. The chin/shoulder on the instrument.