The Rosh Chodesh Torah reading comes from the first 14 psukim of Bamidbar 28. These verses are split into 3 sections in the Torah, but we have to split them into 4 aliyot for leining. The three sections are through 8, 10, and 14.
There are various rules about how exactly psukim can be split up, but essentially, each aliyah must be at least 3 psukim, and we shouldn't start or stop within three psukim of a paragraph break. [In case someone comes in and sees that they started 2 after the break, they could assume we read 2 psukim for an aliyah, and vice versa for someone walking out.] See, for example Megilah 22a.
The common way of splitting the 4 aliyot is as follows (inclusive indexing): 1-3, 3-5, 6-10, 11-14. [We go back and read the third pasuk again.] The second aliyah starts at #3, so that seems to be a problem for the people coming in!
There is another opinion (Gra?) that does as follows: 1-3, 4-8, 6-10, 11-14. True, we now end up reading 6-8 twice, but at least we avoid the other problem.
What basis is there for the first method? Why is it the more common one, as opposed to the second?