I am not sure it is actually simultaneously relayed to the referee. Or, relayed to the referee before the commentators know, anyway.
That is because it is my understanding that the commentators not only hear the realtime official coms, but they can also see the VAR review feed with the actual offside lines as they are being drawn and positioned (which are now not shown to fans, either on TV or in the stadium). And the referee is certainly not seeing that live video feed.
So, in the case of offside, there are instances where the commentators know the outcome of a VAR review before even the referee is told by VAR. It is usually only a second or two before, but it does happen.
Now, technically it is only an official decision when VAR tells the referee, but that doesn’t mean it doesn’t cause confusion for fans when the commentators announce it before the referee hears and indicates on the pitch.