What is obligatory for someone who accidentally swallowed water during a Ramadan day after I pressed the bottle for him to wash his face? And what is obligatory for me?

You bear no sin if you did not know he would drink.

As for him, if he broke his fast due to a legitimate Shar'i excuse, there is no sin upon him for breaking the fast. However, he erred in openly doing so, due to the resulting slander against him and the wounding of the feelings of those who are fasting. Furthermore, weak-willed individuals might be emboldened to imitate him. Hence, jurists have stipulated the disapproval of one who openly breaks the fast.

However, if he broke his fast without an excuse, he has committed a grave sin, and it is your duty to advise him and remind him of Allah.

As for water entering his mouth and being swallowed unintentionally, there is nothing upon him and his fast is not invalidated by it, as the Prophet, peace and blessings be upon him, said: "If anyone forgets and eats or drinks, then he should complete his fast, for it is Allah who has fed him and given him drink."