[Coda]

Originally Posted by Potironette

Then, is it just that the force comes from the person just pulling on the string to pull on the ball into the direction the person wants the ball to go to once in a while?

More or less, yeah. You can't model it as an object on a fixed pivot with an infinitely thin, infinitely flexible, perfectly inelastic tether. You either have to give the tether some stiffness (at which point you're modeling an object on a rod instead of an object on a string), or you model it more realistically:

When you're spinning an object around on a string, you aren't spinning it around a fixed central pivot. You're pulling it at an angle, applying the force in a circle around the center of rotation. The string isn't parallel to the centripetal force vector or perpendicular to the tangential velocity vector; you're pulling on it to one side in addition to towards the middle.