The choice oh the publication time range is only a displaying one. As the tooltip says: "With this [weekly option], the plugin will display in the stats all the published posts from the beginning of the week to the current day (week starts on Monday). This will be the default setting: you will still be able to change the time range the way you want it. You should select this if you usually pay your writers weekly." Again, it's just for displaying, it doesn't delete anything after a week or anything like that.
Future release 2.0 will include the feature to stop the payment amount at a certain point, to set a maximum payment. Is this what you are talking about?
Have a nice day,