D/C engineering designes the trans.
D/C purchasing buys the parts from who ever can supply them at the specified price and to the quality requirements of D/C.
D/C (probably although a subcontractor might) then assembles the parts.
YOU could build the transmissions if you had the equipment to make the parts. I'm willing to bet that the parts that make up the trans come from several vendors. Clutches, springs, gaskets, hardware, castings, fabrications, machined shafting, etc.