Why do I need to pay 700$ in taxed to MA if I didn't receive any income there? I just moved there in August

Income that you earn while living in Massachusetts is taxable to Massachusetts - even if you earned that income in another state.

If you didn't earn any income while living in Massachusetts from August to December, you don't need to file a Massachusetts tax return at all. Part-year residents are only required to file a return if their Massachusetts income is more than $8,000. (See: Who must file a Massachusetts return)

If you did earn more than $8,000 while living in Massachusetts - even if you actually worked in another state - you will need to allocate your income between Massachusetts and the state that you moved from so that you're only paying tax on just your Massachusetts income. Make sure you go back through the income allocation screens to ensure that you've properly allocated your income.