Some people observe the fast of Ramadan one or two days after the date that is announced in Saudi Arabia. Is this correct based on the hadith that a Muslim is expected to synchronize with the people of their own region, otherwise it is a sin?

If the majority of people in your area follow the local sighting of the moon for fasting Ramadan, it is better for you to fast along with them. [1] If you chose to follow the global sighting elsewhere, it is permissible, but not preferable if the majority of your area does not follow it. [2] The claim that it is a sin not to follow the local sighting followed by the community is incorrect. There is no hadith that states this.

References: 

[1] http://islamqa.com/en/38101

[2] Dr. S. Al-Sadlaan, Fiqh Made Easy, pp 86-87