Takes a long time and a lot of resources to simulate and render! It is really just here to show the logic bricks used.
Using bender physics to shatter objects on collision only.
After the voronoi cell shatter has been applied to a mesh, you are left with a few hundred separate shards. Using bullet physics in the blender game engine, all of the rigid body physics for each shard are disabled using a "delay" sensor with a duration of 1 frame attached (using an AND operator) to an "edit object" actuator which disables physics for the shard. This still allows other objects to interact with the object as an obstacle but will not allow it to react to collisions or gravity.
Each shard is then given a "Collision" sensor set to react to other objects with a named property. This is attached (again with an AND operator) to an "edit object" sensor which reinstates rigid body physics for that shard.
Finally the named property you used above is applied to the three balls and each link of the chain, with a radius of influence high enough to activate a shard when it is very close to it.
Now when the simulation is run the swinging of the balls and their collisions cause the jugs to break apart in pieces.
I didn't really make any effort to conceal the cracks. The gaps in the voronoi cell fracture are minimised by making the initial mesh huge. This means that relative to the geometry and the division needed by the bullet physics engine, the gaps are tiny. As a result the simulation must run for many thousands of frames. once these frames are recorded they are scaled down using the dopesheet to make everything seem more like real time as appropriate to objects of jugish size.