If the clients are scheduling these reminders by accessing your website using a browser, I believe you could rely on Javascript to transform the time they choose into UTC. If that is the case, you might construct your reminder-creation form to use Javascript to translate their selected time into UTC and just store the UTC time directly on your server. I believe this would require your users to have properly set time and timezone on their computer. You should check out https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Date
NOTE: It's tricky in Javascript to try and calculate time zone offsets. Just use it to translate a user's local time to UTC.
If you can't rely on Javascript helping you out, then you are going to need to know the date, time, and TIMEZONE where the customer wants their notification. Ideally, you'd have them choose one of the PHP timezones:
http://www.php.net/manual/en/timezones.php
If you know which of those timezones applied to a user, your server can take a Date, Hour, Minute, and Time of day to construct a UTC DateTime.