Network based automatic time update is mobile provider dependant.

The change for summer time is programmed into the handset to happen locally, that would occur even without a sim or a network connectiom.

Openntp is the best answer, why use the mobile network clock when you can get a near direct feed from an atomic clock?

The mobile operators use ntp to set their clocks, just if the time signal gets delayed sending i do not believe they adjust, ntp does account for this.