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.