It is not autimatically cancelled. Working Visas are cancelled by the employer not because they want the ban to take effect immediately but because they intend to use the visa again to new employees. In your case, your company has a handful of available visas, so cancelling your visa was not a top priority.
Your only option now is to get a NOC from your previous employer, otherwise the ban will only take effect after they cancel the visa or when the visa expires. GOOD LUCK.