The screenshot you included shows 6 hours from June 1, which is today.
Exacty what do you mean when you say that the timesheet is not including your recent hours?
This looks up-to-date.
If you are logging additional billabel time, then the hours are showing up on your timesheet within an hour after you log the time.
Keep in mind that hours logged for fixed-price contracts don't count. And hours logged after you have reached the maximum number of hours per week won't show up in this particular timesheet, although they do show up in your Work Diary.