The media count on the store front is not "instant", it is only updated every so often by the store. If you wish to manually update the count right away you can do so in the manager -> settings -> utilities area. Even after clicking on the update media count button, you may not see the change right away until you reset your sessions. To reset your session visit your store front and press ctrl + R on your keyboard. Once you click the update media count button any new visitors to your store will see the newest count at that moment.
There is no settings in the store to make it count all the time for each visitor so they see the newest count. The reason the store only counts every so often is so it doesn't overload the MySQL. You can think of it as a snapshot, the store takes a snapshot of the count and shows that to users. It will then later on in the day take another snapshot and show that and so on..