I think what is happening is as follows (and I hope my explanation is not too confusing):
Lets say that two frequencies are to be analized by the receiver and are arranged such that the lower frequency is the same as the pulse repetition rate of the transmit pulse and the higher frequency is a harmonic.
If the higher frequency is not a small multiple of the fundamental pulse repetition rate, the energy content being radiated at this higher frequency is just too small (a consequence of the Fourier series expansion of a contant repetition rate pulse train) to be of practical use in detecting a signal back from the target. In other words, there is just to little oomph being transmitted at that frequency (compared to the fundamental) to obtain a response back from the target with a good signal to noise ratio.
To get around this problem, the DFX (and I think the Ex does the same), the transmitter is designed so that instead of generating a constant repetition rate pulse stream, it varies the repetition rate periodically. This has a profound effect in the Fourier spectrum being generated. By choosing the change in repetition rate correctly, one can dramatically increase the energy content of the desired higher frequency. The problem is that this "energy peaking" is not constant, but it occurs at specific repeating times, which is of course related to when the transmitter changes repetition rate.
Thus, in order to anlyze the signal at this higher frequency, one needs to look at it at the correct time. We need to take a sample of this higher frequency signal coming back from the target, in a manner that is time correlated to when the trasmitter circuit is generating the maximum amount of energy at this higher frequency . Note that the analysis is still one that we think of as frequency domain (that is we want to generate the ratio of the X and R components of the signal), except it has to be done at the right time relative to the transmitter.
I think this is what causes the confusion about time domain versus frequency domain. Hope the above was understandable.