Ignore the error. That is for a log that is not required. The big news is that you are now sync'd to within 0.000628 seconds of the time reference. You don't have to use time.apple.com. Any of the published time sources will work just fine. Do notice the error number since if it is too large then the time update may not be that good. I would be particularly concerned if you are using a VPN or a ships' internet. If you are using a VPN keep in mind you want a time source close to the VPN outlet (e.g. if you are using a VPN in that connects to the internet in Australia then pick ntp1.anu.edu.au or au.pool.ntp.org which are not on the previous list).
Remember that if you have an iPhone and have cell coverage you can tell your Mac to use your iPhone as its wifi source. Thus you can do a final check and/or time sync while you are set up at the site.
Let's say you have done one of the actions above to set your computer's time. How do you know it is correct?. For that you can use time.gov. If you look at the circled black panel to the right of the page you will see your clock error displayed. If you do not have reliable internet service then you will have to fall back on using GPS as described below.
Once again this seemed so simple...
One of my frustrations has always been that the time in the camera is never synced to the correct time nor has (reliably) the resolution to be useful. I found this again as I tackled this problem. Despite the camera claiming to have millisecond resolution, time stamps are only one second. And only a handful of cameras allow the program to set the time (although Canon written utilities can set it in a broader range of cameras.)
I provided a tool that allows you to set the time in those cameras that allow it and at least display the time in those that don't. The program will optionally try to set the camera time via a Camera Preference in those cameras that allow it.
However I do not have confidence that setting the time resets the entire counter.
Thus if you want to know when your picture was taken I suggest you use the log file. That records a time stamp immediately before the command to press the shutter. It has an accuracy of 0.1 sec and is as accurate as your setting of the run time.