I've had this problem a couple of times in the past 2 - 3 years. Using a given browser (usually Chrome because that's what most folks use), a given user will see the QuickBuild build and build log timestamps with an incorrect time. Normally an hour or two ahead or behind the correct local time. All other users, and all other browsers (e.g. Firefox, IE, Safari), have the correct local time.
The problem (I can't take credit for this, one of my colleagues figured it out) is the QuickBuild cookies. There are two cookies that must be deleted: QuickBuildBrowserTime and JSESSIONID. The QuickBuildBrowserTime cookie sometimes has the incorrect time zone. Even though the JSESSIONID cookie is supposed to expire when the QB session ends, sometimes it will persist.
I'm not sure if the incorrect time zone is caused by daylight savings time not being correctly recognized, or if it is caused by the user connecting to QB from a different time zone when traveling. I have not been able to nail this down yet. Whatever the case may be, while running the browser showing the issue: logging out of QB, deleting the two cookies mentioned above, then logging back into QB corrected the problem.