15-20 seconds would have been plenty, if the watchstanders are sharp, and on the ball, as I assume the IDF guys are.
Here is the doctrine aboard the FF I was stationed on, for a late reported missile. Once the threat bearing is known, via ECM or a lookout, the OOD immediately turns to put the threat, 20 degrees abaft the beam, or about 110 relative, if the missile is coming in on the starboard side. This creates the greatest separation between the ship, and the missile, without presenting a large radar cross-section. Next, SRBOC (chaff) and/or Flares are launched on the side away from the threat, in this case, the port, so as soon as the ship clears, there is a large bloom, astern of the ship, if it's a radar or IR missile.
At the same time, when a missile call is heard, the system is brought out of standby, and if nothing else, the CIWS is quick. About 2 1/2 seconds, and it can acquire a target, and be ready to fire.
Probably some brown stained pants on the bridge, because it all happens so quick, but only a near miss detonation, or near miss destruction, can explain how the ship survived, and yes, the Israeli's read our tactical doctrine, including missile defense. It goes a long way to explaining why the damage is on the stern, and apparently, on the far side of the flight deck. A large chunk of the missile, probably went ballistic after the explosion, causing the damage.
I am sure the IDF's must be very similar.
I still want to find out if the reports about the systems not being active are true. I find that impossible to beleive or consider in such an environment. We shall see. As it is, I have come tobelieve at this point that these picks do not represent pics of after action damage.