What model? Is it both atomic and solar powered?
Casio’s atomic watch lineup includes ones with solar cells, along with other tons of innovations.
This one’s atomic-solar:
As for the Oceanus brand, it is owned by Casio.
Waveceptor WVA-510TA. The watch face is a solar cell, which is able to provide the watch with all the power it needs, provided you leave it on a window sill once in a while. Every morning, at 00:00, 01:00, 02:00, 03:00, and 04:00, it tunes in to WWVB on 60khz in Fort Collins and sets itself. My watch reports that it last reset itself as of 02:03, which indicates good reception (it takes 60 seconds for WWVB to send the time, and the watch listens three times). Bad reception would be 02:06 (or yesterday, if the sunspots are acting up badly I'm in Massachusetts).
When you travel, you don't reset the time on landing. You reset the zone offset, and the hands move rapidly to reflect the new time.