Praise be to Allah.
Standing on the water that falls from the body whilst doing ghusl or wudoo’ does not invalidate wudoo’, because the water that falls from the body during an obligatory ghusl or wudoo’ is taahir (pure).
In fact, even if we assume that this water that falls from the body is najis (impure), such as if there was a hole in the roof of the bathroom from which some impurity fell down, and some of that fell onto his body, then his wudoo’ would not become invalid just because of that. Rather it is invalidated by the impurity that comes from him himself, not by any impurity that may fall on him.
See the answer to question no. 12801 .
If any dirt, or even impurity, gets onto any part of the body after purifying oneself completely, the dirt can be removed by washing it off.
Muslim (317) narrated that Maymoonah (may Allah be pleased with her) said: I brought the Messenger of Allah (blessings and peace of Allah be upon him) water to do ghusl from janaabah. He washed his hands two or three times, then he put his hand in the vessel and poured some water over his private part and washed it with his left hand. Then he struck his left hand on the floor and rubbed it vigorously. Then he did wudoo’ as for prayer, then he poured three handfuls of water over his head, then he washed the rest of his body. Then he moved away from the spot where he had been standing and washed his feet, then I brought him the towel but he refused it.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: He washed his feet somewhere else, meaning that when he had finished ghusl, he washed his feet somewhere else, not in the place where he had been standing.
The apparent meaning of the author’s words indicate that it is Sunnah in all cases, even if the place is clean, as in our bathrooms nowadays.
What appears to me to be the case is that he should wash his feet somewhere else when necessary, such as if the ground is muddy, because if he does not wash them his feet will become contaminated with mud. This is supported by the fact that the Prophet (blessings and peace of Allah be upon him) did not wash his feet after ghusl in the hadith of ‘Aa’ishah. "Ash-Sharh al-Mumti‘ (1/361)".
And Allah knows best.