I will admit it’s been quite a while since my blood bank days, and I will allow that practices vary from place to place, but unless things have changed drastically since I did training as a clinical pathology resident, which included too much time (for my liking) in transfusion medicine edification, whole blood transfusions are not the norm. At the very least, it is not optimal.
The reasons are several, but the main one is that patients usually do not need all blood components to address their immediate problem, and so it’s much more beneficial and efficient to deliver only the part(s) they do need. My leading caveat again notwithstanding, most whole blood nowadays is separated into packed RBCs and plasma (which even in their now reduced volumes relative to whole blood are indeed quite useful), and the platelets are separated off and pooled from several units. The plasma can then be further separated into cryoprecipitate, in which certain clotting factors are conentrated.
Individual hospitals may order whole blood from a blood bank, and that may have been what you transported as a driver, but the receiving hospital blood banks may have then further processed those whole blood units into components.
It is also possible that they may have transfused the units whole, as whole blood is still used in some circumstances. But, as said, unless things have changed a lot, or unless the institution that trained me was off in its own world, transfusion of whole blood is the exception, not the rule.