Understanding PLL VCO Integrator Phase-shift
Is it the control voltage? But, then that's a DC voltage, right?


If it were a DC (non-changing) voltage it wouldn't be any good for controlling anything.

Where we'd see 90° phase shift is if in your graph instead of varying \$V_{control}(t)\$ with a step function, we varied it with a sinusoid. Then the \$\phi(t)\$ function would also be a sinusoid, and it would lag the \$V_{control}(t)\$ signal by 90°.