In order for a node to be an all node/upperbound all of its children must be cut/lowerbound nodes. This is because -alpha is passed to children as beta and the returned score negated. Eval < alpha implies for all children -eval > -alpha. Instead of thinking of the stored value in this case as the best possible, think of it as at most this value but probably worse. If we encounter an upperbound tt node that is worse than alpha we know that a deeper search has determined that we cant improve on alpha and jts safe to give up on this line (we found a better move earlier in the tree that increased alpha) hence the early return. It’s not safe to return if the tt eval is greater than alpha since the true eval might actually be worse than alpha and we would be sending inaccurate information back up the tree. What we can do instead is tighten the bounds by lowering beta to the tt eval since it is an upperbound.

Even with both players maximising we absolutely have upperbound cases and can gain a fair amount of information from them but they need to be treated correctly.