psb a post containing my proposed solution to what you describe. This is by no-means an exact solution, as there is the central assumption that population is equally spread across the county.
Re: Determining population inside a polygon - Esri Community
You can do this using the Tabulate Intersection (Analysis)—ArcGIS Pro | Documentation tool.
Input Zones Features - your commuter zones
Input Class Features - Your county polygons (assumed you've already joined your population data table to the feature class shapes) (also ensure you make the join permanent by exporting the data after joining).
Sum Field - Population number field from your county features.
This would give you the number of estimated persons per intersection of each zone and district.
Each zone may return multiple rows (i.e. 1 for each district it intersects) so you would have to add those row values together.
This is also all based on the assumption that the population is evenly distributed within each district - something you can't avoid unless you have more data e.g. residential dwellings or urban area polygons, then also again you have to make the the assumption that population is evenly distributed within each urban area or residential point and so on and so on...
