Spitter spiders are like all the other spiders, they belonged to a spider farmer before they all got exposed to noxious chemicals that made them grow to the size of a man, with some of them (like Consuela) being even bigger.
In beginning of the film where Joshua, the spider farmer, showed a kid named Mike his spiders, including Spitter Spiders, they were being fed crickets by Joshua. After Mike left, Tank the Tarantula bites Joshua and then the other spiders kill him. They then start to grow to the size of adults.
Tank and the other spiders attacks the town and chasing other peoples to Prosperity Mall
Tank rips open the steel gates that the humans are using and allows the other spiders to attack the humans.
It's legs are seen pushing a tracter that the humans were using to block the spiders away, and then the smaller spiders chase after the humans. The Spitters are killed along with the other spiders in the explosion.