I understand PLLs will match the frequency of the local oscillator to
the carrier via maintaining a constant phase difference between the
received signal and the local oscillator but for coherent demodulation
the phases of the oscillators need to also be synchronized(at least as
far as I understand).
If the frequency is matched by the PLL, then the phase difference must be constant (other than for slow moving phase-drift that is being corrected for because phase-drift means frequency-shift and the PLL that you describe can correct this).
Depending on the type of phase detector the "natural" or neutral phase difference may be at 90 degrees or 0 degrees. For instance, an XOR gate used as a phase detector will naturally settle on 90 degrees as the "locked-in" position but a phase-frequency detector like below: -
Will naturally settle at 0 degrees. Picture from here.
The bigger problem comes when you don't have a carrier (such as with many phase modulation schemes). That's where a Costas loop comes in but there are other methods.