There isn't a time sync being done between the LMS and WeBWorK. Typically each server would sync time with a network time protocol (NTP) server. If a server isn't regularly syncing with an NTP server then the system time can drift, which causes problems with certain activities between servers where timestamps are involved (LTI is one example. Another one I've run into in other contexts is file creation and permissions on network file shares).
In your case (in addition to the new pull request that Glenn referenced), you can check if the server time on your WeBWorK server matches the Moodle server. WeBWorK displays the time at the bottom of each page, so that's easy to verify. I'm sure that there are activities in Moodle that record a timestamp, so you would just have to run one of those and see if the time matches what you see from WeBWorK.