So as your intuition has clearly told you, there will be a change in pitching moment, you're correct, however, exactly how big this change is depends on the aircraft and how it's being flown. Im not familiar with the Red Bull stunt, or the aircraft involved, but if the airbrake is sufficiently near the centre of pressure (CoP) on the airframe, even if it, say, increase drag by 30%, if the airbrake is only 20cm from the CoP, the CoP won't move very much, and the pitching moment will be quite small. Equally, as some commenters have pointed out the stunt pilots will have practiced this many times, and may know precisely how much back stick to input to counter the airbrake...
Now onto the way CoP position affects stability. you may already know, but if an aircraft's CoP is behind it's Centre of Mass (CoM), its is considered stable, this is because if there is a sudden disturbance (say a gust of wind) causing an increase in lift, the aircraft will pitch down, reducing the angle of attack, and reducing the lift produced, countering the effect of the disturbance, likewise if the CoP is in front of the CoM, a disturbance will cause an exacerbating motion, requiring sophisticated active controls (many computers) to counter. (This is a slight over-simplification, obviously, in level flight the CoP is exactly on top of the CoM -or else there would be a moment on the aircraft- since the true CoP is the sum of all pressure forces, wings, tail, the lot, so in reality we are talking about the positioning of the main aerodynamic devices on the aircraft, in particular the wings, in relation to the CoM). Moving the CoP up or down will not have any significant effect on stability because the lift force acts perpendicular to the direction of flight, so the moments involved are only interested in the perpendicular distance from the CoP to the CoM, which in this case is longitudinally. Now, there is also the drag force, which will produce moments depending on where the CoP is up or down, since it acts parallel to the flow, but it tends to be an order of magnitude smaller in size than the lift force (typical airliner Lift to Drag ratios are about 17-18 in cruise, gliders closer to 20 and fighters more like 12). In all off this, remember that aircraft have tail surfaces though, which are constantly being moved about to tweak the CoP and put it precisely in the place the pilot requires, either by direct use of control surfaces or trim, depending on the size of moment the pilot wishes to produce or counter.
In terms of increased 'flow' when pulling up, I'm not quite sure I totally understand. It is true that deflecting a surface to produce a moment will turn the aircraft in relation to the airflow, and this will change the area exposed to the airflow, or increase the drag coefficient, or both, this will change the size of the drag, and also the size of the moment on the aircraft, but again, most forces don't produce huge moments on the aircraft, and if they so, there are always big control surfaces to counter. This is perhaps obvious, or aircraft would depart from flight all the time!
I hope some of that is helpful!