Time based correction aligns the impulse responses of the driver groups in multi-way loudspeakers and/or the main loudspeakers and subs. I should point out that the TacT does indeed have the capability to do this, but the measuring tool needed is obscured in the basically undocumented "dual domain" module and it is generally not an automatic process, at least if you want it performed properly.
I thought the DEQX had the ability to do this too, but maybe it doesn't ? Maybe John Ashman, mac, or other DEQX owners can comment.
You can time correct main speakers and subs with the RCS 2.2X pretty easily, as it will measure the physical distance and any phase discrepancies between the mains and subs on its own and correct them. What it won't do automatically is calculate the additional delay needed by the mains when a DSP crossover is implemented. DSP crossovers are more precise but slower than passive crossovers, and the output of the low pass can lag the high pass function by 1-30 msec depending on both frequency and slope! See the graph in my gallery to determine this delay then add it manually to the main delay figured by the TacT and you should achieve main-sub time alignment. The graph only works for symmetrical filters (i.e. same frequency and slope on high and low pass).
Time aligning a multi-way speaker is more difficult, because you have to bypass the factory crossover and multi-amp. The RCS with TacT digital amps, in conjunction with some powerful but free add-on software called TACS, does time and frequency based correction very well. Based on measurements of each driver group and listening impressions, you can choose the ideal crossover frequencies and slopes and then adjust the phase/delay of each driver group so their impulses align perfectly.
Very, very few speakers are time aligned stock from the factory. A few that claim and may actually be are time aligned include the top models from Vandersteen, GMA, Ascendo, and Wilson. The vast majority of speakers that claim to be time aligned fail because of simplified baffle design and the use of 2nd or higher order filters, which require one or more drivers wired out of phase to achieve reasonable frequency response.
Although the only way to build a truly time aligned speaker without DSP, first order crossovers severely stress the drivers as the are forced to operate cleanly over large frequency ranges. DSP gives the benefits of first order networks (actually even better because of the zero group delay -- the derivative of crossover-induced phase change -- of FIR crossovers) to higher slopes that will either improve a driver's performance and allow a larger selection of drivers to be used.
Here is an interesting system using a big collection of TacT equipment (with TACS) for frequency and time based correction. The TacT gear replaced about $1,000,000 worth of Accuphase, Gryphon and Cary gear
http://www.aca.gr/pop_jyk.htm