Heirayon = conception NOT birth.
And so the reasoning goes that the world was conceived in Tishrei and created in Nissan"
Rambam's son Rav Avraham cautioned us to neither be too literal nor too cynical regarding Aggadah.
Illustrative digression
If I were to say charcoal = diamonds a literalists would lug worthless charcoal to 47th street and expect to make a huge profit.
Scoffers would say: charcoal = diamonds?! That's outrageous!
Wise people would say:
Hmmm what's the point? Can't be literal. Then after delving into it they would realize that where there's charcoal there be diamonds (at least potentially)
End of digression]
Michdi Let's see. The first mishnah in Rosh Hashanah lists 4 New Years. So both Nissan and Tishrei are already enshrined as New Years. The question about conception and birth must have some symbolic lesson. I don't know what was originally meant. Here is a shot at it anyway.
The physical universe in the northern hemisphere is reborn every Spring. It is no wonder that Christians observe springtime as resurrection time. Mother Nature is doing it simultaneously! So physical (RE)birth is springtime
Autumn is a time of harvest, of completion, of impending winter hibernation. It is a time of taking stock financially and also spiritually. The autumn New Year is not about birth, but of reflection, and introspection.
Now map it out
Autumn = Tishrei = conception = intropsection
Spring = Nissan = birth= = rebirth
Tishrei the world was conceived because it entered "God's Mind" metaporically speaking
In Nissan evidence exists of physical creation or re-creation.
The words of the wise Hazal can be cryptic. Being overly literal misses the point; and. scoffing also misses the point.
Zissen Pesach
RRW