Is it obligatory to make up the day a Muslim fasted with the intention that it was a day of doubt, and then it later became clear that it was the first day of Ramadan, due to the different moon sighting methods between states?

The start of Ramadan is confirmed by sighting the crescent moon or by completing Sha'ban with thirty days. Astronomical calculations are not to be relied upon. The fundamental principle for sighting is with the naked eye, but if it is sighted using modern instruments, then that sighting is to be acted upon.

If the crescent moon is sighted in an American state that shares a similar moon-sighting horizon with your state, then you are obliged to fast with them. The majority of scholars hold that fasting is obligatory even with differing moon-sighting horizons, but the more preponderant opinion is to consider the difference in horizons.

If you are informed of the moon sighting after dawn and you had not formed the intention to fast during the night, then you must abstain from food and drink for the rest of the day and make up that day, according to the majority of scholars. However, if you had intended to fast with a general intention, such as "If tomorrow is Ramadan, then I am fasting," then your fast is valid, and you are not obliged to make it up, according to the preponderant opinion.