In a Generator, why when the Exciter voltage increases the Generator Voltage decreases?
There are two sets of conditions tabulated in that table, open circuit voltages (7V exciter, 267V output, 8V exciter = 297V output and 9V exciter = 340V output), so about 37V at the output per volt on the exciter terminals.  

We also have a set of values under load :


30V = 267V @ 1575A
29V = 297V @ 1415A
28V = 340V @ 1235A


Now all of these values equate to about 420kW, which more or less makes sense for a constant torque on the prime mover.

Using our earlier estimate of a factor of 37V/V for the voltage scale factor a naive model would have the following output voltages: 


30V * 37V/V = 1110V
29V * 37V/V = 1073V
28V * 37V/V = 1036V


So what accounts for the difference? 

Lets try modeling it as a series resistance (Or series inductance so it does not dissipate power), I will use the resistor model to demonstrate, but the inductor is probably closer to reality. 

Voltage dropped across our supposed series impedance :


@1575A 1110V - 267V = 843V @ 1575A = 0.535 ohms.
@1415A 1073V - 297V = 776V @ 1415A = 0.548 ohms.
@1235A 1036V - 340V = 696V @ 1235A = 0.563 ohms. 


So it looks to me like an acceptable model (for some things) is a dependent voltage source having a gain of 37V/V in series with a resistor or inductor having an impedance at the operating frequency of ~0.55 ohms.

What you are seeing is that the voltage drop across the machines impedance is at some currents greater then the extra terminal voltage from the increased excitation. It is interesting to draw a load line for constant power output and to plot on it the required exciter current to hit that power level for various load impedance values.