Volume or size of the last trade will dictate a possible change in implied vol surface.
So, if an OTC trade is only for a small size... smaller than the quoted size on screen, it wouldn't affect much. If it's 10x or more... you will start to see a shift before it actually trades. That's because there will be a few market makers involved in taking the OTC trade and if they start to find out what the other side wants to do, sell/buy and at roughly what price, they will quote accordingly.
So definitely real-time.... otherwise you wouldn't be pricing at the correct/current market (fair) value.