Dunno about Kaplan, but I used to teach for The Princeton Review (SAT, GMAT) and basically if you wanted to tutor any grad/professional school exams (GRE, LSAT, MCAT, etc.) you had to start out as a ho-hum SAT tutor. I presume that's just to prove your ability to handle a classroom. With TPR, you didn't have to provide any scores outside your old SAT ones. Instead, you took one of their diagnostics and if that was good enough, you sat through a compressed version of the course (good for you if you hadn't taken the actual exam yet) before teaching.
As for pay, it's better than anything you'll find on campus unless you're an engineering or IT wizard. In San Diego, pay started at $14/hr (for SATs) and went up to something like $20/hr for MCAT and LSAT. TPR salaries vary from city to city, partly because some are privately owned. Anyway, I would imagine Kaplan has comparable salaries or else no one would work for them.
Keep in mind, most classes are at night or weekends in hotels and whatnot all around town, so you'll be driving and working during hours most people would rather be at home. And there are other responsibilities that go along with teaching, like grading exams, preparing lectures, etc. that take time . . . time you're not paid for.
