In Webmail Enterprise Edition Version: 16.3.6628, if you add an item to your Calendar you must click to another view or refresh the page to have it show up. For example, if you add an item while in Day view, you must click Month, Agenda, All Appointments, or refresh your browser window to see it; it is not visible on your calendar until doing so. This should auto-populate client-side without the need to click to another view.
Also, if you add an appointment while in Week view, sometimes it will not show up in Day view, other times it will. However, if you do get it to show up in Day view, and click back over to Week view it will sometimes disappear from both Day and Week view again. If you click around between views enough it will show back up. It is very hit or miss. Tested in both current versions of Firefox and Chrome, and they both behave the same.
UPDATE: This appears to be an issue with email as well, and seems very hit or miss. When receiving new email, there will be no indication that new email has arrived unless you switch folders or reload the page.