This has been a bone of contention in various airlines I've worked for; types B737 and the B757/767 family.
Boeing say:
Close TL's etc etc,
Raise speed brake
Apply max reverse thrust.
etc. etc.
It does not say how to raise the speed brake. Some training dept's. insisted it was to be done manually BEFORE the T.R's were actioned. Others said that the raising of the T.R's to the interlock position would deploy the speed brake before the application of reverse thrust and thus satisfied the sequence of events by automatics. i.e. the way Boeing designed the system to be used.
It was a controversial point when changing companies. It is certainly more natural to apply T.R's immediately after closing the T.L's because that is where your hands are.
However, as often the case, getting a definitive answer from Boeing as to the correct method was impossible. They would not, according to the respective training depts, declare any preference but approved both methods.