It seems that the generator refuses to accept storage types other than chests or barrels.

To test it, I used the following mods:

• Applied Energistics 2 (no bus or interface could not interact with it)
• Storage Drawers (similarly, the generator could not put the content in drawers, even through a layer in the form of drawers controller)
• Extetded Drawers (exactly as with the last two, no reaction

In all cases, the generator just kept the cobblestone in his inventory.
In my opinion, this is a bug. But if not, it is still an omission that such a nice mod does not work with the above.