Klothys’s Design affects only creatures you control at the time it resolves. Creatures you begin to control later in the turn won’t get +X/+X.

If an activated ability or triggered ability has an effect that depends on your devotion to a color, you count the number of mana symbols of that color among the mana costs of permanents you control as the ability resolves. The permanent with that ability will be counted if it’s still on the battlefield at that time.

Hybrid mana symbols, monocolored hybrid mana symbols, and Phyrexian mana symbols do count toward your devotion to their color(s).

Mana symbols in the text boxes of permanents you control don’t count toward your devotion to any color.

Colorless and generic mana symbols (, , , , , and so on) in mana costs of permanents you control don’t count toward your devotion to any color.

If you put an Aura on an opponent’s permanent, you still control the Aura, and mana symbols in its mana cost count towards your devotion.

The value of X is determined only as Klothys’s Design resolves. Once that happens, the value of X won’t change later in the turn even if your devotion to green changes.