Is there something wrong with my new GMT II?

[Rolxism]

Hi I have purchased 4 Rolex's over the years subs dj ect. My newest piece I have been very excited for. When I received it after winding and putting on I thought everything was perfect. I wore it for about a week everyday. After taking a small break and putting it in the safe, when I get it out and I wind it to get it going again I noticed I am winding it and the seconds hand isn't starting to move. After winding it for about 10 seconds and pushing the crown in and closing it down it takes about 3-4 more seconds then the watch starts. All my other watches the power supply can be dead and I shake the watch on my wrist and they will start. Or if I wind it for 1 twist with the crown out still they will start working. Is this new VERY expensive watch broken ? I have spoken to DavidSW about it and he said he's had that with a couple of watches he's had in the past and is willing to ship it to Rolex for me to get it checked out. Has anyone else experienced this where you wind it and it doesn't start right away? After the watch is going everything seems to be perfect holds time and keeps going as long as I wear it everyday. Its just freaking me out that something might be wrong with this, as I don't want to ship it if I don't have to. Any advice very appreciated.