Wa alaikumusalaaam
Note first that the astronomical birth of the moon is one thing where as the sighting of the crescent on earth is another thing which follows the astronomically defined birth by some hours or more than a day.
Your colleague had mentioned to you that it should be on two different days maximum (next day).
The sighting of the visible crescent of the new moon from earth can be on three different days on earth as was the case this month beginning of Ramadan. You can find this by studying the maps that I presented on power points in the Ramadan Knights Fiqh Course in Melbourne. Those maps were taken from the website,
www.moonsighting.com which is a well known website in these matters. Also you can verify that with other sources from Muslims and non-Muslims too and from a matter of fact.
Example of this monthThose maps show that the moon this month was to be seen clearly on the night of 31st August, i.e. the night before 1st september in South America. Then on the night leading to 2nd September in Australia, India, Indonesia, Saudi Arabia, US etc. As for Scandinavia and Russia and northern parts of UK or lot of it, the crescent of the new moon could not be sighted until the night leading to 3rd September.
That is three days to sight the crescent from Earth for this month of Ramadan.
That is why scholars from the earliest times said that when sighting the moon, you go by the sighting of areas which share the same moon-rise. This is one of the two main opinions in this matter, and from my memory this is a saying of Imam Shafiee among others.
As for this much, you can study the maps and refer to others as something that is a matter of fact.As for the astronomical explanations, I'd refer you to the above mentioned website itself where they can give you detailed explanations of these matters. Or ask others who devote their time to the astronomical aspect of these. From what I understand though, briefly, the reason for this being on three seperate days and not just two seperate days (one day and the next day) is due to the tilt in the axis of rotation of the earth. You can see therefore the countries that see the moon this month first are the ones in South America, then the central parts of Planet Earth and finally the norther parts - due to the tilt it seems. However you should check for the explanation of why with astronomical experts and not me. As for it occuring on three seperate days, that much is well established from the practise and from the maps, as I wrote above and you can check those references to discuss with them further about the astronomical aspects.
Wassalamualaikum