Can PokeBank or Transporter pull from Diamond / Pearl (gen 4) ?
No, you'll need to transfer them to a Gen 5 game first.
>>27232101
So PokeBank works with a gen 5 game? Or do I need to send that Pokemon from gen 5 to gen 6?
>>27232359
You can send Pokemon from gen 3 all the way up to current games, but you'll need to have a gen 5 game to interact with Transporter.
Transporter will send them to Bank, where you can pick them up using a gen 6 title.