Related for Chullin 209:58
מים ראשונים ואחרונים חובה אמצעיים רשות ראשונים נוטלין בין בכלי בין על גבי קרקע אחרונים אין נוטלין אלא בכלי
They said this only of [hot] water wherein the hand is not
Tosefta Berakhot
Washing [hands] before [the meal] (Mayim Rishonim) is optional. [Washing hands] after [the meal] (Mayim Acharonim) is obligatory. [When he washes] Mayim Rishonim, if he wants to interrupt [the water flow over his hands and pour the water over them the second time] he may do so. [However, when he washes] Mayim Acharonim, if he wants to interrupt [the water flow over his hands and pour the water over them the second time] he may not do so, [but rather he must pour the whole cup of water over the hands in one shot].
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