Earth rotates under the sky
Right ascension and declination describe celestial positions in an Earth-equatorial system; altitude and azimuth translate those positions into the observer’s local horizon. The conversion uses the time plus the observer’s latitude and longitude.
Sources: U.S. Naval Observatory — Computing Altitude and Azimuth
Longitude and clock time are coupled
Longitude changes local hour angle, while civil clock time must first be translated into the correct astronomical instant. That is why an apparently small timezone or daylight-saving mistake can shift the rendered orientation even when the date is right.
Sources: U.S. Naval Observatory — Computing Altitude and Azimuth · IANA — Time zone and daylight saving time data
Precision should match evidence
Exact inputs are valuable only when they are supported. If the time is approximate, or the birthplace is known only to a city, record that uncertainty instead of manufacturing extra decimal places.