My players are starting to use spirits, and I want to make sure that I get this part correct.

Let's say that the spirit has already been summoned and is in astral. At the beginning of combat. Would it go something like this? I always made the assumption that when the spirit attacked it would just materialize for free (or something) and attack on Initiative 26.

Initiative Order + Action:

Spirit: 36. Action: Waiting

Magician: 25. Action: Command Spirit (simple action) to attack Mook with Elemental Attack.

Mook: 20. Action: Something...

Spirit: 26. Action: Materialization (complex action)

Magician: 25. Action: Starts wishing his spirit would show up faster.

Mook: 10. Action: Something...

Spirit: 15. Action: Elemental Attack (complex) against Mook.

Rest of combat.