All perfect praise be to Allaah , the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Your Wudhoo’ is valid and you are not required to do anything else. Nevertheless, the scholars of Fiqh stated that the intention has to be made before performing the first obligation of Wudhoo’ (washing the face). Al-Hajjawi, may Allaah have mercy upon him, a Hanbali scholar, said: "It must be made before performing the first obligation of Wudhoo’." This means that it is not valid to delay making the intention for Wudhoo’ after performing the first obligation. In other words, if one performed any of the obligations of Wudhoo’ before making the intention, it is invalid and it has to be repeated.
This does not mean that Wudhoo’ is invalid when making the intention precedes performing the first obligation. Rather, some of the scholars stated that making the intention when washing the palms at the beginning of Wudhoo’ is recommended. Al-Buhooti, may Allaah have mercy upon him, a Hanbali scholar, said: "It is recommended to make the intention at the first recommended act in purification, such as washing the palms at the beginning of Wudhoo’."
This indicates that you misunderstood the words of the scholars of Fiqh.
Allaah Knows best.