You're on right track, just put your Person ID field on details shelf then you'll be able to see all the marks in you map.
Let us know if this help.
If you follow this link it is pretty easy to do. Keep in mind that creating a spider diagram or map requires two rows of data for each origin and destination. This is how the line gets out and back from the starting point. Without that second row, you wind up with a radar map.
Update: I finally tried this but it did not work.
This is my map right now:
Only one dot shows.
(Record ID = Person ID)
This is what I did:
Creating 2 new parameters (Station Lat & Station Long) that accept a list of values set from Departure Lat & Arrival Lat and Departure Long & Arrival Long respectively. I then created a calculated field from those parameters and set the geographical to lat / long for each parameter and dragged Station Long in column and Station Lat in rows. The problem: it only shows a single point on the map, which I'm guessing is the average of all the values from the parameter
Try to put any other dimension which contains territory information in detail shelf and check. Else share some sample mock up data in packaged workbook.