Exactly Herman! What you've stated is the crux of the argument FOR time coherence. What I stated is the over simplified reasoning given by designers who use steep filters.
They point to "phase coherence" but the only thing they are measuring is sine waves.
As far as "alignment" versus "coherent" go, well, maybe just semantics. Thats fine. I'll go just one step further using a different explanation from another designer and then let it be. Because to each their own.
Anyway. This is how Pat McGinty basically explained the difference in his mind.
Take two drivers, a tweeter and a midrange and you mount them on a flat baffle. Connect the positive leads together and the negative leads together. Take a 9V battery and tap the leads against the battery. The microphone will see two distinct upward spikes. (assuming you touched positive to positive, etc.) Then you start to slant the baffle backwards an increment and repeat the battery test. The result is that the spikes will converge a little bit because the acoustic center of the tweeter physically leads the midrange and, assuming the tweeter is on top, the more you slant it backwards the more the tweeters acoustic center moves backwards towards the acoustic center of the midrange. Perpendicular to the horizon is the frame of reference here.
Anyway, at some point the microphone will see one convergent spike. This is what they consider the physical time alignment of the two speakers. And this was basically the first step of the design process used by Meadowlark, once they decided on the drivers they were going to use.
So at this point the drivers acoustic centers are aligned at the precise point in space that the microphone sees them as one.
So if you now apply a good and appropriate first order filter to the drivers you should end up with a fairly accurate step response. This is what they consider time coherent because it is the only way that all frequencies arrive at the microphone (or ear) at exactly the same time. And, actually, Meadowlark's were pretty good at this.
But, if you applied a fourth order filter as was the case with the Hales Transcendence Five speaker that I referenced. (And also once owned) you end up with a step response like what you see in the Stereophile article. If you bypassed the crossover in those Hales and set up a microphone at a normal listening level at a normal listening distance and applied the 9V battery test (Note: you aren't trying to pass DC through the drivers, only create a "tick" response by quickly touching the leads) you would see a single spike from all the "ticks" arriving at the same time.
But you pass music through the steep crossover on the way to those same drivers and what happens is that, because of the steep filter, you see the tweeter lead the mid, and the mid lead the woofer. In this case the acoustic centers of each driver are time "aligned" but the speaker is not time "coherent".
Anyway, as I said, these are the distinctions that Time Coherent designers make. And, like Pat McGinty always said, "All you really need to do is look at the step resonse because if that isnt right then nothing else matters." And, for better or worse, these were the decisions and distinctions these guys made. The fact that there are so few who make speakers like this is a very loud statement as to the importance the industry as a whole grants these principles.
Cheers!!