It looks like you're doing a join on zip code and you want to be doing a union or full-outer join created with non-matching attributes. That will give you a separate row for every point and every zip code polygon in your dataset.
I wrote up some instructions on how to make this type of dual axis map with Tableau geographies (your zip codes) and lat/lon points. I think this might help explain how the dual axis works. Dual Axis Mapping - Many Ways
I also made a quick example using your file. I've attached it so that you can check it out.
Claims Map_v10.5.twbx 133.2 KB
This looks great! Thanks so much!
However, for some reason I am not able to bring up the number of records for each of the zip codes now (lighter shading for lighter volume, darker shading for higher volume).
It works for me to shade the zip codes based on number of records (assuming picture below is what you were trying to do)... my best suggestion without seeing what you're seeing is that you might have dropped the Number of Records measure in the wrong place. With the dual axis, make sure you're dropping it on the axis with the zip code polygons.