I received a notice of change in tax return, the return adjustment reason is withholding credit has increased says Massachusetts income tax withheld of $331 does this mean I'll be receiving this addit

Yes, if the $331 represents additional withholding, you will be receiving an additional refund if they didn't report other changes (i.e. increasing your income.)

About how long does this take to receive it? Will it be deposited like my initial refund was or a mailed paper check?

I got this same letter. 8a. unemployment compensation and 37. Massachusetts income tax withheld. Do I owe money?

What did the letter show?  Your situation is a little different because your letter is also showing an increase in income.
If you had additional income that wasn't reported on your Federal return, you may need to prepare and mail an amended return.