Ross - can you include some screenshots with the explanation.
I've tried to compare between ArcMap and Pro what you're describing. Here I have selected 2 features from my airports, and I want to select the Points that intersect ONLY SELECTED airports.

We see that I get the two Points selected that we expect:

Now in ArcGIS Pro, I have selected 2 airports.

I have three big green Points, none of those are selected. Since I want to select the big green Points that intersect only the selected Airports, I'll select the PointNotes in the Contents and click Select by Location.
The tool opens and I set it up like this:

It runs and honors the selection, giving me the two selected points that I expect.
In ArcMap, the Select by Location dialog is not a geoprocessing tool, so needs user input about how to handle a selection. In ArcGIS Pro, this is a geoprocessing tool, and geoprocessing tools honor selections.
If this doesn't help, what are we missing? Could you provide a similar explanation along with screenshots?
Thanks