Following a SQL Server backup or restore job being run, the number shown on the LiteSpeed console screen is a little slow to update.
For the Job & DTS statistics window to be update the job itself needs to be fully completed before the appropriate tables are completed and updated. You then wait for the normal refresh of the Console before the details are updated on the console screen.
For most of the statistics you can change the refresh rate for the Enterprise Console by the view menu and options choice. There is an option for the Refresh stats every xx seconds. The Job and DTS statistics are slightly different and will get updated once the tables have been populated. You can force this by right clicking on the instance in the Enterprise Console screen and selecting the option
Refresh Job Statistics.