aabm01:
I'd want to use the NTP server option
That won't help you. That would turn your Yun into a time server so that other computers could access it and get the time from it. This is the opposite of what you want. You want the NTP client mode, which is enabled by default.
At this time the 'advanced configuration panel --> System --> System --> Time Synchronization' is set like:
That looks correct, but uncheck the server box: it doesn't get you anything, just uses up more resources on the Yun.
How long take the Yun to check the date/time to the NTP server?
I ask this because if the configuration above is Ok it's supposed, after a while the date/time would have to be correct, but it doesn't
It should run all the time in the background, and periodically update the time, but I'm not finding any documentation on how often it does this. To make sure you have things running properly, try this command on the SSH command line:
ps | grep ntp
which on my system gives:
1649 root 1496 S /usr/sbin/ntpd -n -p 0.openwrt.pool.ntp.org -p 1.openwrt.pool.ntp.org -p 2.openwrt.pool.ntp.org -p 3.openwrt.pool.ntp.org
31880 root 1484 S grep ntp
The first line shows that the ntpd process is running, and it has the the options to query the list of servers, just as you have it configured. (The second line is just the ps | grep command itself running.)
The official documentation on ntpd (scarce as it is) is here: NTP client/ NTP server [OpenWrt Wiki]
One option to speed it up is to manually request it to update the time, for example:
ntpd -q -p 0.openwrt.pool.ntp.org
This will request a time update now, and then quit once it has set the clock (you don't need to keep it running, since the automatically started process is still running in the background.) You could add this to the startup script to run each time the system boots by going to the System --> Startup tab of the advanced configuration pages, and adding it to the Local Startup file at the bottom of the page.
I tried a quick test running it manually. I changed the time, ran the command to resync the time now, and then verified the new time:
root@Yun4:/# date
Thu Oct 15 10:02:49 EDT 2015
root@Yun4:/# date 10:00
Thu Oct 15 10:00:00 EDT 2015
root@Yun4:/# date
Thu Oct 15 10:00:02 EDT 2015
root@Yun4:/# ntpd -q -p 0.openwrt.pool.ntp.org
root@Yun4:/# date
Thu Oct 15 10:00:11 EDT 2015
root@Yun4:/# date
Thu Oct 15 10:00:14 EDT 2015
root@Yun4:/# date
Thu Oct 15 10:03:13 EDT 2015
root@Yun4:/#
Looks like it took about 5 seconds actually re synchronize the clock (after running the ntpd command, I entered the date command every 2 or 3 seconds until the time changed.