Yes, in this example, when you resolve step 4 of the attack, the dice you rolled in step 3 do no damage. Then the first corrode effect of the jelly's attack does one point of direct damage instead of putting on a corrode marker, and then the second corrode effect of the jelly's attack does one point of direct damage instead of putting on a corrode marker.
Now we check triggers and discover that the jelly has both attacked and damaged the zombie in step 4. This is where I think the reconstruct ability happens.
Importantly, I'm arguing that the Jelly caused the damage with its attack, and that the direct damage from the attack is damage from the jelly.
This is unlike bashing into a wall because bash is a separate attack received by the bashed creature, and is resolved in a separate attack sequence. But direct damage is not an attack, it's an effect, and in this case it happens within the attack that causes it, like the push effect itself.
If the attack and damage trigger is only checked in the middle of step 4, after the dice rolled in step 3 do no damage, but before effects from the attack are resolved, then I can see that the "attack and damage" clause might fail, but usually Mage Wars checks continuously and the direct damage caused during the remainder of step 4 is still part of the same attack, and direct damage is still damage.
I guess I'm taking "attack and damage" literally. Did it attack? Did the attacked creature receive any damage during the attack? I realize that this is unusual, especially if you're used to MtG which has a separate concept of "attack damage" thats different from all other sources of damage, but as far as I know, Mage Wars doesn't have that concept.