Brainlocity uses your phone's time zone to know what day it is for you. If you travel, the app adapts to your new time zone without you losing your streak or your progress for the day.
Changing time zones doesn't give you an extra day: your daily counters are kept. To prevent abuse, very frequent time zone changes don't apply immediately, and your account's region (which sets some free-version conditions) doesn't change automatically when you travel.