There are 4 rules that would cause the postponement of the 1st day of Rosh Hashanna from being on the day of the molad. One of the most commonly implemented rules is called Lo Ad'u Rosh, meaning that Rosh Hashanna cannot occur on the 1st, 4th or 6th day of the week.
The reason for not allowing it to occur on Wednesday or Friday is to prevent Yom Kippur from occurring on Friday or Sunday. I've been able to locate the Talmudic discussion on this.
I understand that the reason to prevent it from occurring on Sunday is to prevent Hoshannah Rabba from occurring on Shabbat so that we could beat the aravot. I haven't been able to locate the Talmudic discussion on this. I found a web site that referred me to Bavli Talmud Succah 43b and 44a. To me it seems to focus on whether and why using the aravot were forbidden on Shabbat in the 1st place. But, I don't see any mention of adjusting the calendar to make sure it doesn't happen. Did I miss it, or is this discussed elsewhere?