Explaining the solution for this treetop area puzzle

Your understanding of the square symbols is correct: they fail if they share a region with a square symbol of any other color. Non-square symbols don't matter in the least.

However, your understanding of the spiky symbols is slightly off. The spiky symbol must share a region with exactly one other symbol of the same color (but any kind of symbol is fine). Symbols of other colors don't matter at all. I think this is the first puzzle where it matters that the other symbol isn't necessarily another spiky symbol.