I was not sure about it at first, but thanks to your topic I looked into it and I hope the following explanation will clear up your confusion:
The “waveform” you have mentioned shows the amplitude in time, so it is the “time domain” signal. And you can see the difference between the waveforms (or the time domain signals) of PSK and MSK in the images I formerly attached (and you’ve mentioned it was clear to you).
When it is said that MSK is continuous-phase, the phase in here refers to the phase in time domain signal (or the “waveform”). This has nothing to do with the constellation points phase, as the constellation shows the signal in space domain (or in vector domain), and not in the time domain (MSK has more similarities to QPSK in terms of encoding, rather than PSK).
Regards