If your time zone has changed, you will still receive your medication reminders, and you will still be able to track your medications through the Today tab.
Your reminders will come at your locally scheduled time. For example, if you scheduled your medication in Chicago (Central Time) for 7AM and you travel to New York (Eastern Time), you will receive your medication reminders at 8AM while in New York. On the Today page, you will notice that your 7AM medications now show for 8AM.
Update: We are actively working on a new time zone feature that will give users an additional option to receive reminders at their originally scheduled time. For example, if you scheduled your medication in Chicago (Central Time) for 7AM and you travel to New York (Eastern Time), you would be given the choice to receive reminders at 8AM Eastern (as described in the previous paragraph) OR at the originally scheduled time (7AM Eastern). This feature will be released in a future version.