Don't talk to participants' supervisors unless the participant knows that you're doing it, what you're going to talk about, why you're doing it and what the likely impact will be on them. Except in mighty peculiar circumstances, you would be well advised to invite the participant to the meeting.
If it works in the context of the meeting, start by thanking the supervisor for approving his/her direct report's involvement in your project. ("Jane, I want you to know how much it means to my project for Sam here to be involved. By helping adjust his responsibilities so he could participate, you've really done a lot towards making our deadline possible.")
Consider using the project flowchart to draw attention to the interlocking nature of the milestones and the impact that a delay on his/her direct report's contribution would have on the project and its participants.
Close the brief meeting with a confirmation request; eg. "Jane, I'll let you get back to your work here. I just wanted to confirm that Sam will be set to spend 9 hours during the week of the 27th to complete milestone 'J'. (Pause as he waits for Jane to confirm) Thank you so much!"