It is not correct that we must spit out the food/drink in our mouth if we still are eating/drinking at the time when fajr comes in.

Imam al-Albani, rahimahullah, stated:

'So therefore from the Fiqh that is to be criticised, and which runs contrary to this Sunnah, is that a person says, "If someone hears the Adhaan and has some food in his mouth, then he must spit it out." So this is over strictness, and (ghuluww) exceeding the limits in the Religion, and the Lord of all of the creation admonished us, and reminded us, in His Book and in the Sunnah of His Prophet, sallAllaahu alaihi wa sallam, that we should not exceed the due limits in our Religion. So He said, in the Noble Quraan:

O people of the Book! Do not exceed the limits in your religion, and do not say anything about Allaah except the truth.

And our Messenger sallAllaahu alaihi wa sallam, said to us, or he, sallAllaahu alaihi wa sallam, said, "Beware of (ghuluww) exceeding the limits in the Religion. Because those who came before you were destroyed by their exceeding the limits in their Religion." So when Allaah¹s Messenger, sallAllaahu alaihi wa sallam, has made it clear to us that there is in the matter of a persons taking suhoor, latitude and a margin of ease, to the extent that he said, "If one of you hears the call to Prayer whilst the vessel is in his hand, then let him not put it down until he has completed his need from it."

So it is opposition to Allaah and to the Messenger that a person says that one who hears the adhaan whilst he has food in his mouth must spit it out upon the ground. This is not from the Sunnah. Rather this is contrary to the Sunnah, and is contrary to the clear command of the Messenger, sallAllaahu alaihi wa sallam.'

From http://www.spubs.com/sps/sp.cfm?subsecID=IBD09&articleID=IBD090005&articlePages=4

Shaykh Muḥammad Ibn Sālih al-ʿUthaymeen, rahimahullah, said during his commentary of this Ḥadīth:

This Ḥadīth can be explained from two perspectives:

[1] That the muʿazzin calls the aẓān based upon an estimation, like those who call the aẓān presently. This means that he may or may not call it at its correct time.

[2] That the muʿazzin calls the aẓān based upon certainty. This [i.e. continuing to partake of the suhūr while the aẓān is initially being called] is a concession. When a person raises a vessel of water to drink from it, he becomes attached to the water, so from Allāh's mercy is that he can fulfil his craving. Therefore, if the vessel was on the ground [or on the table during the onset of the aẓān], he shouldn't pick it up to drink from it. The water vessel must be in your hand; otherwise, you will not be attached to the water you are about to drink.

Similarly, if food was brought in front of you before the imām started praying, then you should partake of the food, even if you miss the prayer [in congregation]. Because you have become attached to the food that was placed in front of you [prior to the congregational prayer], praying in congregation no longer becomes compulsory.

Shaykh ʿAbd al-Muḥsin al-ʿAbbād (حفظه الله) stated:

'If the mu‘azzin—whom people rely upon to know the prayer times—begins to call the aẓān and a person was already drinking something, then he should finish his drink. He shouldn't, however, start to drink after the aẓān. Hastening to start to drink something upon hearing the aẓān is impermissible, since the aẓān occurs after the time for prayer enters, and eating and drinking after that time is prohibited. The fajr prayer is legislated at that time because it is the time of dawn. As for eating and drinking at that time for the one desiring to fast, then his time has expired for doing that.

Therefore, if the mu‘azzin calls the aẓān and a person is drinking, he should finish his drink; however, if he didn't start to drink, then it is impermissible for him to start drinking.

It is said about this issues: “What is permissible to continue doing may not necessarily be permissible to start doing” meaning, starting to drink [on the onset of dawn] is impermissible; however, if a person had already started to drink, he can finish his drink. This doesn't mean that he should expel what is in his mouth and cease from drinking; rather, he should swallow whatever was in his mouth and finish his drink, since the One Who specified the time interval for fasting is the very One Who exempted this scenario. Therefore, what is permissible to continue doing may not necessarily be permissible to start doing.'

From https://www.troid.org/ibadah/siyam/ramadan/2427-a-clarification-of-some-common-doubts-and-misconceptions-affiliated-with-the-month-of-ramadan