Well, i'm not sure what I am or am not supposed to be able to see, but when I log in to the operating website on hotspotsystem.com, the “summary” page shows me the last 10 transactions, and I can click a button at the bottom of the window to “show all transactions”. So maybe my account is just skrewed up.
In any event, I might have figured out what was happening… maybe. One of the employees where I set up the hotspot disabled the WiFi on her smart phone after previously using the hotspot. Now, for some reason, when she opens her web browser without using WiFi, she is still taken to the splash page… maybe it's saved in her history or something, so it goes there automatically, or it was left open previously. In any event, maybe it's possible that the uses this splash page to log in, initiating a new “transaction”, but does not create a new “session” because she isn't connected to out WiFi. This might explain why these mysterious IP addresses that I see on the transactions look like they belong to the cellphone carriers according to WHOIS.