There is no fundamental difference.

The rest length is the default length of the Spring when there is no force applied to it.

Of course differences in the rest length will result in a different physical interaction and visual appearance. A certain length may have chaotic effects within the context of your program and so will large changes in length. So I think it's not so much about the moment of setting the value, but more about the value and the context in which it operates. Apart from the question, why change the rest length after initialization?

I cannot explain why setting the same value it already has causes crazy behavior. But I cannot reproduce it either. If you have a runnable example that shows this behavior, it would be easier to comment on this problem. Right now, I suspect it's a specific problem to your code, rather than a fundamental issue with rest length. But like I said, that's just speculation without the code.

A general way to dampen the effects of forces within the physics system is to increase the drag.

p.s. I really like the clear documentation, the color palette and the design sensibility of your tumblog.