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 is His slave and Messenger.
It is permissible to rub the face or one of the limbs which must be washed in ablution after washing it the third time, provided this does not lead to Waswasah (satanic whisperings). However, it is not permissible to wet the hands and rub the face or the limbs after the third washing as it is confirmed that the Prophet performed ablution (washing each part) three times and then said: “This is how ablution should be performed, and whoever exceeds this limit [washes more than three times], he is wrong and has indeed transgressed the limits and committed evil.” [An-Nasaa'i, Ahmad and Ibn Maajah].
In our view, the person whom you referred to in the question suffers from Waswasah and what he does is not permissible unless he is sure or predominantly thinks that the water did not reach the part which he wanted to wash, in which case he must wash that part. However, doing what is mentioned in the question on a continuous basis, is evidence that this person is afflicted with Waswasah, and we have already issued Fatwa 83401 about the treatment of Waswasah, so please refer to it.
Allaah Knows best.