Three definitions first (simply): CoW (Centre of Weight) and CoP (Centre of Pressure). These two govern the aircraft (any) while flying (lets forget about thrust and drag now - the other two). AoA (Angle of Attack) is the anlge between the leading edge and the relative airflow.
In case of airplanes CoW and CoP are close together. For a Paraglider, CoW is significantly below CoP (normal flying). So it is possible that when AoA changes, CoW "moves out" from below CoP. The natural behaviour of all constructs in the air that CoW "wants to be" below CoP.
The difference between normal and reflex profiles is what happens when AoA change.
Let's say you hit an uplift stream (turbulent air going upwards).
This will increase AoA.
In case of "normal" profile, this will result CoP move FORWARD. But, hence CoP "wants to" be over CoW, the whole glider will "slide backwards" a bit. This will increase the AoA even further, which will move CoP even forwards etc etc. It would cause the glider to stall, but by the time it would stall the pilot's pendulum will stabilize the system.
So in rough air, normal gliders "move a lot".
In case of reflex profile, CoP moves BACKWARDS instead of forwards, moving the glider itself forward above the pilot, which decreases AoA, so the two effects negate each other. That is why reflex gliders are more easy on rough air.
The fact that they are faster has nothing to do with profile.
Reflex gliders have different line distribution and different sizing, but these are independent "changes". Okay maybe not completely independent - a reflex glider, when fully trimmed in, has "almost like" a normal profile - to easy the job with takeoff and landing. But this means that they will get their relfex profile, once they are trimmed out, so weight is distributed towards the front lines. But the more full-bloodied reflex glider you get, the less this is a compromise.
IF you overload a normal glider, it will be fast as any relfex glider.
Also worth to note that reflex is more difficult to open once closed up for any reason. But they fold much harder.