Does the imam prostrate for forgetfulness if he makes a mistake in the prayer but stands up before completing the three tasbeehs?

The questioner : Okay, our Shaykh, there is a man who, during the prayer, in the middle of a rak'ah, after completing the third rak'ah, sat down believing in his mind that the prayer had ended. So, after the people praying behind him recited the tasbeehs for him, he got up and brought in the fourth rak'ah, but he did not prostrate for forgetfulness. So we asked him why he did not prostrate? He explained that the sitting he did not exceed the three tasbeehs. So here, it is supposed to mean that he sat for the prostration of forgetfulness, or as he says: that the three tasbeehs are necessary?

The Shaykh : I mean, is the prayer four rak'ahs?

The questioner : The prayer is four rak'ahs, yes.

The Shaykh : Okay, so instead of standing up to the fourth immediately, he sat down.

The questioner : He sat down, yes.

The Shaykh : As if he wanted to sit in the third, in the third of Maghrib, for example!

The questioner: Yes.

The Shaykh : Then they recited the tasbeehs for him.

The questioner: Yes.

The Shaykh : Then he stood up. The detail you mentioned about this has no basis, first of all. And secondly, the prostration for forgetfulness is upon him and it is necessary, due to his saying (peace and blessings be upon him): .

The questioner : May Allah reward you with good.

The Shaykh: Is it clear?

The questioner : Clear, Shaykh.