Well, what mean by “on the same network” maybe more complicated then it sounds if a device has multiple network interfaces and a non-trivial routing such as any modern smartphone that smartly switches between wifi and cell. It’s plausible that various apps and devices have a different behaviour which network they treat as local/standard.

However, I just tried it out with two Samsung Androids. One is a hotspot and has no other wifi. The other one uses the hotspot (and not other wifi) obviously. Then lauching pairdrop, they can “see each other” (through broadcast packages I assume) on the local network. During testing the hotspot device had internet access through 5G, so both devices could reach paridrop.net, but I believe, this is not needed while in local network mode. At least the file transfer itself should not go through the internet in this mode.