Why do the subs produce sound up to almost 500 Hz? You're getting close to having voice in the subs (voice typically begins around 500 Hz
The graph shows the frequency response of the subs run with a low frequency pulse that extends to 400hz. The crossover (shown in pink) has not yet been applied. When the correction is calculated from the measurement, the target curve is adjusted to incorporate the selected crossovers. With the filters I use, response in the subs is down -6dB at about 64hz and falls off 36dB/octave beyond that. So at 128hz they're down 42dB. And the inverse goes for the mains below 64hz, where they naturally roll off since the woofers are sealed. Trust me, you do not hear any voices coming from the subs. They blend in so well with the mains that you do not hear them at all, until you put in some program material that has massive LF signal and then they make themselves known to everyone in the house

Why is there such a dip at 20 Hz? I would think that those massive subs would produce more output at 20Hz.
Well, the subs are driven by a Crown K2 with adjustable input sensitivity. I have it set to match output with the mains after correction in the amps, i.e. -3dB at 20hz. I could add add another 12dB output to the subs which would raise their response (blue and purple traces) cruves up quite a bit, i.e. +9dB at 20hz, without changing the shape of the curve. But why would I want to do that ? The TacT would just have to attenuate it back down to match the output of the mains. Also there is a dominant room node at 40hz and another at 77hz which exaggerate the output at those frequencies, making the bottom end roll off look steeper than it actually is. Like any woofer, output at 20hz is lower than at 400hz. This doesn't matter, since output beyond the bottom two octaves is eliminated by the crossover. Only thing that matters is potential output at the frequencies you want the subs to reproduce.
Compare the output of these subs to that of another "full range" speaker I used to own, measured at the same distance in the same room. Of course I wouldn't expect them to have the output sensitivity and extension of these huge sub towers, but in their case the low bass falls "off a cliff" below the lower room node of 40hz, despite having two large carbon fiber woofers, one with oversized motor, and a large passive radiator. And in case anyone was going to ask, adding or removing a few milligrams of putty (even a few grams of putty) made no difference in the measurements.

I take it that the top graph of the dual domain shows the impulse response of the filters used for correction. How does the TACT actu ...
The top graph of the DD screen shows the impulse of the measurements, not the correction. There are 10 buffers loaded with data, the upper graph shows 5 & 6 while the lower graph, which does show the correction filter in the frequency domain, shows 7-10. I could load the correction filter in the time domain and post a screencap of that.
As to have the TacT convolves its filters... you'd have to ask Boz himself ! And I have a feeling he won't be willing to share that information. One thing I know is that correction resolution is dependent on frequency, below 400hz Fs=3khz, 400-3khz Fs=12khz, above 3khz Fs=96khz.