First of all, Chrono24 doesn't sell watches directly -- they are just a site to facilitate individuals and dealers to sell watches. They run an escrow service to facilitate a safer transfer of watches and money.
Second, the dealer you bought it from said they "checked the movement and pressure tested it". This is different from a complete service and overhaul. The basically do a check to make sure the watch operates, doesn't look horrible of a timegraph (and may simply adjust the movement so it DOES look good), and run a pressure test (probably dry) but don't necessarily replace all the gaskets.
For peace of mind, I would send it in to Omega for a complete overhaul. It's a 12-year-old watch and the original owner(s) likely never serviced it. A lot of people sell their watches when it's time to get them serviced because they don't want to deal with it. The watch will come with a two-year warranty and you can be guaranteed it will have been properly serviced.
Or, you can just wait and see until it demonstrates bad timing, gets water inside, or stops working and then send it to Omega for service. I wouldn't bother with the 1-year Warranty from the dealer. Who knows if they will actually service it, or just do what they need to to get it running again.
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