For the web browser Team Site or Team Site Mobile App:
The game times of a team will not change with a change in the users timezone in their profile or the change in timezone on the phone. It shows local times for events -- local being the timezone for the website the schedule is published on.
For calendar subscriptions:
Some people don't use Team Sites and just use the "Subscribe" feature to put games into the Outlook or Google Calendar. People viewing their games like this will probably see the game times change when they travel and change timezones.