At whatever time of day you call the API, data always starts at 0:00. Either UTC or the time zone you selected.

Many weather APIs follow weather model runs. Therefore in the evening, data suddenly starts at 12:00 UTC regardless of the timezone. It is quite a pain, if you want to build an app displaying todays data, but in the evening you do not get data from the morning anymore.

With Open-Meteo multiple weather model runs are merged together and partly overwritten. At around 4:00 UTC, the first weather model with data starting at 0:00 UTC arrived (usually called 0z run). 3 hours later, the 3z run arrives with data starting at 3:00 UTC. After a couple or model runs arrive, it is quite a mix out of different weather model runs. If done right, you notice nothing of this behaviour ;)

    < 0z run >
      < 3z run>
        < 6z run>
          < 9z run>

Data is constantly merged into a time-series. The API then selects the appropriate start time, which is set to 0:00 UTC (or if a timezone is set, local-time at 0:00, which could be 4:00 UTC depending on the utc offset).

Yes, unix-timestamps must be in UTC+0. If a timezone is set, data still starts at "2021-09-13T00:00", but this is now local-time. With a 4 hour UTC offset, I would have to set the unix-timestamp to "2021-09-12T20:00" and the developer has to correctly reapply the UTC offset again to get local time. This can be done, but is prone to errors.