When a Pokemon appears, everyone with in 200 meters should see it on their trackers. To actually see it on map, and have it be catchable, You pretty much have to be right on top of it. I’d say with in 5 to 10 meters.
Everyone will have a chance of catching a Pokemon when it spawns, but after 15 minutes, the window closes and the Pokemon is gone.
Rare Pokemons are especially hard to find, and they don’t show up repeatedly at a spot. The algorithm might be spawning them at popular destinations at a higher frequency, but one would be lucky to spot one per day at one ofbthe hot zones.
People are stampeding because of the 15 minute limit, the fact you need to be right over the spot, and the fact that a rare Pokemon is really extremely rare. I have been playing since the game went live in Taiwan and I have yet to see a Snorlax in the wild, or a Lapras, or a Dragonite, or a Charzard, even after using those so called Poke Radars…