When people talk about phase-locked within EEG, they mean at the same phase relative to some index time (e.g., stimulus onset). I'm having trouble imagining anything 'real' that would be phase-locked (that is, appears in the time-domain average across trials) but not time-locked. Such a signal would have to "know" what amplitude it "should be" at some given point in time, without having made any perturbation to the system you are measuring beforehand.
Let's back up and use a different terminology (also used in your source) and consider EEG responses as evoked or induced, with a third case of phase-reset:
Evoked responses are those that are most easily detected by averaging the time-domain signal across stimulus presentations. Evoked responses are additive to the ongoing signal, so over many trials if you average then the background disappears whereas the added response is revealed.
Induced responses are those that affect the amplitude of ongoing activity. If you average an induced response across presentations, you get a flat line, because the phase is random on different trials. If, however, you do some measurement of signal amplitude, like calculating power, and average that resulting signal, you'll see the response.
Phase-reset is when ongoing activity changes in phase. If you average the time domain signal, a phase-reset will appear like an evoked response, but if you look carefully at individual trials, the magnitude of response depends on the phase of ongoing activity. If the ongoing activity is already at the 'target' phase, there is no effect.
Back to the source you are reading, let's think in terms of evoked and induced signals. Importantly, EEG signals are usually tiny, so describing EEG signals often involves discussing what sort of averaging you might need to do to measure them.
Evoked signals, being additive, can be described as time-locked and phase-locked, though I'd be careful with overinterpreting "locked": there is always going to be some jitter in latency when you deal with biological neural responses.
Induced signals, on the other hand, are those considered not to be phase-locked, in that when you average the time-domain response on multiple trials you won't see any signal. They'll still need to be time-locked to some extent, though, otherwise you again will not detect them across trials. But really, that's where this conversation ends: the discussion about phase-locked activity is really about the difference between evoked and induced. Personally, I prefer the evoked/induced terminology.
These are some good papers on evoked and induced activity. I think David is good with the concepts and has a more formal mathematical treatment, but I like the illustrations of things in the complex plane by Martinez-Montes which I find very intuitive.
David, O., Kilner, J. M., & Friston, K. J. (2006). Mechanisms of evoked and induced responses in MEG/EEG. Neuroimage, 31(4), 1580-1591.
Martínez‐Montes, E., Cuspineda‐Bravo, E. R., El‐Deredy, W., Sánchez‐Bornot, J. M., Lage‐Castellanos, A., & Valdés‐Sosa, P. A. (2008). Exploring event‐related brain dynamics with tests on complex valued time–frequency representations. Statistics in medicine, 27(15), 2922-2947.