In short, YES, Thingsee One will move automatically to the correct time zone and you won't loose any data because of it.
Thingsee device has a Unix time-stamp. This means that the time is recorded in an unique code-number in reference to UTC time zone. For more information on Unix time and UTC time zone check here.
This code is then converted to a human readable value and personalised to your current time zone in the the browser through the internet. In addition, and as a consequence of being connected to the internet, the device will have its Unix time-stamp corrected automatically too.