The email read: "Please contact me when I return from traveling on [this week]. We will review the internship opportunity at that time."
How should I phrase my follow-up email?
As you have requested to be contacted after the date here, I am reaching out to you to schedule my interview for the intern position at department and/or company name. I'm looking forward to working as an intern for project/department/division and contributing to the success of your organization, while gaining invaluable experience.
Looking forward to hearing back from you.
I'd suggest going for a level of formality between the other two answers, although you should take your cue from any previous communications, if you can.
Also, keep in mind that you don't know the reason for the travel - it could be pleasure (vacation), it could be personal (visiting family for good or bad reasons), it could be business (a conference), or any number of other situations. It's best to not make any assumptions about it.
I'd reply to the "please contact me" email with something like this:
As you requested, I'm reaching back out to you to discuss the internship opportunity with
your company. If you would like to reach me by phone, I will be available at
these times. I look forward to hearing from you.
Thank you for this opportunity,
A slight variation would be to replace the last sentence with something like "I look forward to hearing from you once you've had a chance to get caught up," which implies that you understand he might take a day or two to get through all his email and reply.