TOTP algorithm,UTC,and world changing time

[Luca Renaud]

Imagine the server I need to authenticate me (running TOTP authentication)
is hosted in the U.S.,California time for example,and I am in Italy
(smartphone clocked to Italy time).How can the TOTP algorithm,apps deal
with this kind of situation (very usual these days of world
traveling).More,today with cloud hosting and pages being served from
changing data centers around the world (different timestamps) how can TOTP
authentication really work?