Abu Hurayrah quotes the Prophet as saying:

He who vomits involuntarily is not required to fast later on; but the one who deliberately causes himself to vomit must fast later on. (Abu Dawud, Sawm: 32; Al Tirmidhi, Sawm: 25; Ibn Majah, Sawm 16)

There are two kinds of mouthful vomit; one of them is the intentional vomiting, the other is the unintentional vomiting. If mouthful vomit passes the throat by itself because of an illness, then it is unanimously agreed that it does not invalidate the fast. However,, if a person swallows it intentionally, the fast becomes invalid according to Imam Muhammad, though it does not invalidate the fast according to Imam Abu Yusuf.

Self-induced vomiting will break the fast because in such a situation, something more or less goes to the stomach. Such a breaking of the fast only requires compensation (qadha). However, if less than a mouthful vomit goes back unintentionally, the fast becomes invalid according to Imam Muhammad, though it does not invalidate the fast according to Imam Abu Yusuf. If something goes inside intentionally, then the fast breaks according to both Imams.

When self-induced or involuntary vomiting passes inside as a result of one’s own free will and if that person eats or drinks because of it, then it only requires compensation (qadha).

In essence, it is wajib to wait till iftar without eating or drinking when the fast breaks by mistake. Just like after vomiting, the fast which becomes invalid by mistake, eating or drinking only requires compensation (qadha), not a Kaffaarah (atonement).

Even an involuntary mouthful vomiting does not break the fast.