Praise be to Allah.
Rinsing the mouth is one of the obligatory parts of wudoo’; this has been discussed previously in the answer to question no. 153791
It is mustahabb when rinsing the mouth to do it extensively, except when one is fasting, because the Prophet (blessings and peace of Allah be upon him) said: “Do wudoo’ properly, rub between the fingers and go to some lengths when rinsing the nose, unless you are fasting.”
Narrated by Abu Dawood. 142; at-Tirmidhi, 788; classed as saheeh by al-Albaani, may Allah have mercy on him.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: One of the Sunnahs of wudoo’ is to go to some lengths in rinsing the mouth and nose. Going to some lengths in rinsing the mouth means moving the water forcefully and making it reach all parts of the mouth.
End quote from ash-Sharh al-Mumti‘, 1/171
But this going to some lengths is mustahabb, as we have mentioned, and it is not obligatory; rather if the water reaches his mouth and he swills it around, that is sufficient.
Ibn Qudaamah (may Allah have mercy on him) said:
Rinsing the mouth means swilling the water around in the mouth.
Rinsing the nose means snuffing up the water into the nose. Then the water is to be expelled from the nose.
It is not necessary to swill the water around in all of the mouth or to make it reach all of the inside of the nose. Rather that is part of going to some lengths that is mustahabb for one who is not fasting.
End quote from al-Mughni, 1/89
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
It is sufficient with regard to what is obligatory to swill the water around in the mouth a little.
End quote from ash-Sharh al-Mumti‘, 1/172
Based on that, if the individual rinses out his mouth and moves the water around in his mouth, that is sufficient and he doesn't have to make the water reach his throat; rather doing that is mustahabb.
And Allah knows best.