New York State can only revoke or suspend your privileges to drive in New York State. At your arraignment (initial appearance) a NYS judge must suspend your privilege to drive here (NYS) if you had a BAC of .08 or higher OR if you refused to take the breath test. However, 45 states are parties to an interstate compact that requires them to suspend the license of any person who has lost their privilege to drive in another state. These five: DO NOT BELONG to the compact
If your home state has not been notified then they will not suspend.
New York typically does not notify the home state until the final hearing/disposition of your criminal case. Although, if you refused the breath test then after your administrative refusal hearing, where it is likely your NYS privileges will be revoked (cancelled) NY DMV will notify at that time.
If your home state is NOT notified (and they of course must notify you at the address listed on your license) then you still have driving privileges in all 49 states while your criminal case is pending in New York State.
To sum up: either after a administrative refusal hearing with a Judge or at the end of your criminal case your home state will likely suspend your license to drive and you will not be eligible for reinstatement until your privilege to drive in New York is restored. Your home state may also choose to impose an additional period of suspension or revocation for a New York DWI, DWAI, or ADWI conviction. Your home state could also require classes, treatment, an evaluation, fines, and surcharges. You should consult with an attorney from your home state to confirm what may or may not happen.