In regards to 30 Adar I which is the first day of Rosh Chodesh Adar II, Reingold & Dershowitz hold that the birthday in a non leap year will be on 1 Nisan. However many  halachic authorities hold by 30 Shvat since it is the first day Rosh Chodesh Adar  R&D don't state what their reasoning is but logically all dates are always the number of days after the first of the month. The 30th of Heshvan Kislev and Adar I are always 30 days after Rosh hodesh which are 1 Kislev 1 Tevet when 30 does not exist and 1 Nisan which is 30 days after Adar when Adar I doesn't exist. 

Here is an example of molad misinformation for the uninitiated.

First point 

Molad Sivan 5786 is listed on the Chabad site mentioned as being on Shabbat May 16 2026 at 6:02 PM and 15 chalakim. However since it occurs after 6 PM the molad date is really Sunday and therefore if the month had been Tishri, Rosh Hashanah would have been delayed to Monday because of Lo ADU Rosh.

Second point 

Sunset on May 16 2026 in Jerusalem will be at 7:30 PM. So while according to the molad calendar the molad was on Sunday according to the sunset calendar the molad was on Shabbat. 

Third point 

Solar noon May 16 will be at 12:38 PM daylight saving time in Jerusalem. So 6 hours after solar noon the molad day will begin at 6:38 PM day and the 6:02 PM Molad time will actually be at 6:40 PM on every Israel synagogue clock.

Fourth point

The above molad is an arithmetical determination. The exact molad Siban will be Motzei Shabbat at 11.02 PM

The molad announcement in luach ezras torah comes first in pedantic Yiddish but without the secular date and then in shortened English style but with the secular date.

The secular date addition is problematic since the molad change of date is not midnight nor sunset but rather 6 hours after true noon in Jerusalem. And therefore the 3:23 am Marcheshvan (Heshvan in the Yiddish version) molad was not at 3:23 am on the shul clock in Jerusalem but at 15 hours and 23 minutes after true noon Friday in Jerusalem.

In the luach Eretz Yisrael used in many shuls in Israel the above molad is written Molad Cheshvan Shabbat evening 3 hours 23 minutes. Also on the same page is the 24 hour version without minutes ie Shabbat 9 hours 414 parts since the molad Shabbat day began 6 hours after Friday true noon at 0 hours.

In the luach ezras torah the molad is placed at the end of the first week of Cheshvan instead of the last week of Tishri when it will be announced.