The Timesheet page will display the last timesheet that has been opened during that session. If the Timesheet page is opened for the first time after login, the current week timesheet is will be displayed. However, if at that point another timesheet is opened, and the user navigates away from the Timesheet page and returns to it later, that last timesheet will be displayed instead. This is working as designed.
After the user logs out and logs back in to Clarity, the current week timesheet will be displayed.
If this is not helping, might sure the user is using a generic URL to log into Clarity. It might be the user is login to Clarity with a URL pointing directly to an older timesheet/timeperiod (hardcoded in the URL being used).