The activated ability is a mana ability. It doesn't use the stack and can't be responded to.

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

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

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.

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