That's an interesting question.... I am not sure but here is how interpret it:
The card reads "... you may reveal Fumble immediately after the Declare Attack Step. The attack misses and does not affect the target object..."
When you attack, you must follow these steps in order:
1. Declare Attack
2. Avoid Attack
3. Roll Dice
4. Damage and Effects
5. Additional Strikes
6. Damage Barrier
7. Counterstrike
8. Attack Ends
In my opinion, it would work similarly to a defense; therefore skipping to Step 5: Additional Strikes.
It makes sense to me, but I am not 100% sure still because they could simply say "The attack is avoided" instead of "misses and does not affect the target object" .
Cheers,
Lukard