If your opponent Flip Summons “Cyber Jar” while “Non-Aggression Area” is active, because he cannot Special Summon, the cards he would normally Summon that were picked up are destroyed. All the cards picked up with “Cyber Jar” that would not normally be Special Summoned (such as high-level monsters, Spell and Trap Cards, and monsters that are Special Summon-only) remain in the hand and are not destroyed.
If you activate “Non-Aggression Area”, your opponent can still Special Summon THIS turn with “Call of the Haunted”, etc.