To keep it basic - the speed governor on the turbine/engine prime mover determines the MW output. Power In = Power Out (neglecting losses and other fringe effects).
The voltage regulator controls the exciter that provides the excitation that controls the generator output voltage. Raising and lowering output voltage will not change the MW output unless the governor. More Voltage = More MVAr's.
MW and MVAR's are at 90 degrees to each other. Changing one has practically no effect on the other.
MVAR's always flow from high voltage to low voltage. When the generator output is higher than the system equivalent voltage, MVAR's flow out of the machine. If it is lower, VAR's flow into the machine.
I'll leave it to others to draw the generator's internal voltage, current and flux vectors to show how excitation can shift the output vectors.
We are considering a generator that is connected to a large network. The essential is that the voltage at the terminals of the generator is fixed, both in phase and magnitude. Similarly, the frequency is fixed. (The things are differently for a stand-alone generator.)
When the power of the prime mover is increased, it tries to push harder, but because the frequency is fixed, the rotating speed cannot change. Only the position of the rotor (relative to the phase of the voltage at the terminals) moves forward, so that the phase of the internal, induced voltage changes. The result is an increase in the real power of the generator.
When the excitation of the generator is increased, things are a little more complicated. One consequence is that the internal, induced voltage of the generator increases. But because the voltage at the terminal of the generator is fixed, there must be a larger voltage drop in the internal impedance of the generator. Because the impedance is mainly reactive, the result is an increas in the reactive power of the generator.
You mean synchronous generator, do you ?
Output of generator depends on two things: mechanical power input (torque on shaft) and excitation current.
With increase of output reactive power the output voltage is increasing too (other parameters const.). This is due to magnetic field behaviour in the machine (in opposite situation, decrease output reactive power, voltage drops).
Why increasing excitation voltage will increase reactive power output ? Increasing excitation volatege will increase excitation current, obvious. Higher current means stronger excitation field which will interact with stator field. This affects angle between stator and rotor fields (stator current and voltage phasors aswell which affects power factor).
In general: this all comes from synchronous machine construction. It's behaviour can be observed on it's regulation and output diagrams.
"If an experiment works, something has gone wrong"
