Do lure modules and incense cause new pokemon to spawn near you, or existing pokemon to be drawn to you?

When a Lure Module is used on a PokéStop, do existing pokémon in the area get drawn to the PokéStop? Or rather do new pokémon spawn within the PokéStop area of effect? Or both?

When I head to a PokéStop with a lure module, it seems Pokémon appear from nowhere, and the Pokémon listed Nearby don't get any closer. So I am guessing it only causes random spawns.

Has anyone found the lure module to actually draw existing Pokémon to your location, or only spawn new pokémon? And does an individual's incense act the same way?

For an individual's incense, this could be an important question. If I see a rare pokémon 3 'steps' away, I would want incense to actually help draw that pokémon closer to me as I search for it. Whereas if the incense only spawns new pokémon, I'd rather use incense at other times.

jdero's comment is correct, while it may seem like Pokemon are drawn to the lure, they are definitely spawned on the lure. Areas have a list of Pokemon that are more likely to spawn there so you will see that nearby Pokemon are also the Pokemon that spawn at lures. A few factors make this very apparent. Firstly, in an area with multiple lures activated in close proximity a Pokemon will show up ever 5 minutes or so. The natural spawn rate of any are couldn't support this. Second, I have, while being in one such area, seen naturally spawning Pokemon appear every 20 or so minutes(about average) in addition to the ones spawned by the module. lastly, I have NEVER seen a rarer Pokemon move after using an incense or module near it (within 2 paws), and was able to go out and find said Pokemon after the lure was activated nearby in its original spot. Also incense works the same way as lures except instead of a proximity to spawn in, they spawn directly on top of you.