I have heard that Lord Rama was born at afternoon 12 O'clock (In day time) in Treta yuga. Same as in Dwapara yuga, Lord Krishna was born at mid night 12 O'clock (In night time). Both Lord Rama and Lord Krishna were avatara of Lord Vishnu, then what is the need of choosing specific time? They can born anytime, time never bond to gods as per my understanding.
Why did Lord Rama and Lord Krishna choose to born at 12 O'clock in day and in night time respectively?
What is significance of birth timing in both case?
We commonly perform Krishnastami pooja and Ramnavami pooja at same time which I mentioned. I have heard from my elders, those people, who are in "Bhojan or external desires" were unaware of Lord Rama's birth and those people, who are in "Kama bhog" were unaware of Lord Krishna's birth.
I got birth time (12 O'clock) details of Lord Rama and Lord Krishna from one of the article based on "Stotra mantranche vignyan"(page no.25) by Parampujya Swami Savitanand which is published by Prasad prakashan, Pune. Soft copy link for this is not available online, but from here get the hard copy. Scriptures are only defining that Lord Rama was born at mid-day and Lord Krishna was born at Midnight. Beside this I did not find any scriptural reference of exact birth time.