Your parenting plan or decree should say something about who arranges for travel or who should communicate regarding the beginning of parenting time. Your best bet is probably to keep the lines of communication open via written communication (i.e. email) to show that you are willing to allow the non-custodial parent to exercise their parenting time. Also, this written communication will document everything in case an issue arises later.
While your situation seems straight forward from your facts, there may be additional facts that would allow for more thorough advice. As such, it might be a good idea to consult with a family attorney.
DISCLAIMER This answer is general information only. The information presented should not be construed as formal legal advice, nor as the formation of a lawyer/client relationship. I am an Arizona attorney and can only really speak to Arizona law. Please consult an attorney in your state for specific answers. Please refer to Avvo.com's terms and conditions.