They have to implement something like HSR (host state rewind) where the server recieves position data from the client with a timestamp.
When the server says there is an AoE attack it sends the info out to the client.
Now the client can evade as soon as he sees the red zone, and if he makes it out this information is sent back to the server together with the time where the player actually is at this moment.
The server compares the timestamps and now knows that the client was out of the damage zone before the attack.
Or something like that...

They had a similar problem in Mechwarrior Online a few months ago, where you would have to aim very far ahead to hit fast moving mechs. After they implemented such a HSR function and some tweaking the visible and the real position match almost perfect.