I think it has something to do with the 1/60 rule but I don't know what that is.
Let me offer a practical answer to what is a deceptively simple question
If there is only hot soup and no meat, or if there is meat but the milk fell in the soup: if the volume of soup (including any meat) is 60x greater than the volume of milk which fell, the dish is kosher (SA YD 92:2) and you should stir the soup (MT Ma'achalot Asurot 9:10, Kaf HaHayim 92:8). If the soup is not 60x the volume of milk then the dish is not kosher and the pot needs to be kashered.
If there is chicken in gravy and the milk fell on a piece of chicken: if the volume of meat is 60x greater than the volume of milk which fell, the dish is kosher but one should remove a little less than an inch of meat (ca. 2cm.) around the area where the milk fell. If there is not 60x then the dish is not kosher and the pot needs to be kashered
If the milk fell on a piece of chicken protruding from the soup: this becomes really complicated: you have to ask a rav
In all cases one should not add more soup to make up the 1:60 ratio.
This is for Ashkenazim following the Rema that we don't ask a non-Jew to taste and go according to bitul be shishim (SA YD 98:1).
In all cases, you should ask a rav as small changes in the starting situation can have big impact on the halacha.
The questioner is correct.
Shulcha aruch Yore dea 98,1
איסור שנתערב בהיתר מין בשאינו מינו כגון חלב שנתערב בבשר יטעמנו גוי אם אומר שאין בו טעם חלב או שאומר שיש בו טעם אלא שהוא פגום מותר והוא שלא יהא סופו להשביח וצריך שלא ידע שסומכין עליו ואם אין שם גוי לטועמו משערינן בס' וכן אם הוא מין במינו כיון דליכא למיקם אטעמא משערים בס'.
Something forbidden to eat that got mixed into food which was permitted to eat like milk and meat (which is forbidden together) should be tasted by a gentile and if he can't taste the milk it is permitted. Alternatively if it has a rotten taste it is permitted to eat this mixture as long as it won't end up tasting good together in the future. This gentile has to be reliable and if such a person not available one measures if the milk is a ratio of 1:60 to the meat it is pemitted.
Rema Orach chaim 98,1
(ואין נוהגים עכשיו לסמוך אגוי ומשערינן הכל בס) we don't rely o a gentile in our commuities rather we always measure a ratio of 1:60 to permit the milk/forbidden substance.
This also applies to soup with meat (when the meat is a 60th or more of the volume of the soup)even though its not pure meat because the soup becomes a neveila (forbidden like the meat "chanan") in matters of milk mixing with meat Shulchan Aruch 99,3: (note rema says Chanan with every forbidden substance that mixes with permitted substance)
בשאר איסורים חוץ מבשר בחלב חתיכה הבלועה מאיסור מצטרפת לבטל האיסור.
And the rema Yore dea 92,4 says that liquid becomes a neveila in a case of milk and meat mix together.
Coclusion: Ashkenazim follow the Rema who requires a ratio of 1:60 of milk against meaty soup, most Sefardim follow the Shulchan aruch and get a expert trustworthy gentile to taste the soup but if unavailable also require a ratio of 1:60 of milk against meaty soup .
Note: this is only whe the milk falls inadvertently into the meat soup but if one pours it in on purpose the mixture is forbidden see S.A Y.D 99,5.