There is a time frame I think 2 hours that you let the blood collect into the bag and then you remove the bag, attach the administration set and return it to the pt IV. Not sure with chest tubes but have done it with hips.
The chest tube pleur-evac (collection device) has a separate collection chamber on the side in which the blood collects. The side collection bag can be detached and spiked like a unit of blood. The blood cells start to degenerate after they leave the body so they aren't ideal anymore, so auto-transfusion must be done within a brief period of time or not at all. We usually only do it for trauma patients who are trying to bleed out. We don't do this very often anymore since we now have a large volume transfusion protocol where we can transfuse 15 units of blood products in 10-60 minutes depending on IV access...repeat as needed...yeah it's a lot of blood, but patients can bleed out in just a few minutes. Once I gave almost 50 units in less than 3 hours before the doctor could stop the bleeding. We also had to intubate the patient, place a cordis & ngt, go to ct scan, then to interventional radiology for embolization.
And there's a filter in the system so you aren't reinfusing random other crap that might have been floating around in a pleural or other surgical space, like fat or other products of trauma. You also can't reinfuse blood from a contaminated area (like an abdominal multitrauma with bowel tear).
And if you use a blood scavenger system, where the drainage can be "washed" before being infused, the window can be extended to 6 hours. We do this primarily with our open heart patients who need to return to the OR for bleeding, but I imagine it would be the same for thoracotomy drainage (the vast majority of our thoracotomies are for lung cancer, so blood scavenging is not an option, which is probably why I've never seen it done).
Cases when you wouldn't auto transfuse at all:
-infection (don't want to give it "help" to become sepsis)
-probably a couple of others, but those are the two big ones