Time Period formatted line item's will not take Time Range into the consideration instead it takes super set(Time Scale + Time Range) into the consideration.
For your requirement there is a work around in both classic and new ux.
Please find the below steps if you are using new UX
1. Create a Module with Time Range as a dimension and it should be in the Pages of Pivot and one line item time period formatted as year. Write Formula of line item as Item(Time) and then you can use this line item to filter the grids or for any other downstream calculations.
2. In New UX in the card enable the selector from which user can make selection and the line item's data will be derived from this time period selection.