How does the SNAXO decide what frequencies are bass and treble?

It doesn't - without intervention.

https://forums.naimaudio.com/to...-is-an-active-system

"Additionally:-

Naim make their active crossover for their range of speakers and a small number of previously popular (Linn mainly) designs and some "special" commissions.

However, in order to design an active crossover one needs - crossover frequencies, filter slope and relative driver efficiencies. These, alone, do not guarantee a worthwhile result and I would suggest that such a project is best undertaken entirely in the DIY sphere - any Naim "solution" being both expensive and provided entirely on a "best fit to provided parameters" basis.
That is - we could not become involved with any further fine tuning, refunding or ongoing involvement with the project.

A one-off is very much outside our normal R&D and production schedules. I would imagine that, as when last I discussed this, a substantial charge would have to be made, a full payment received and an agreement to no refund (unless faulty).

I would not recommend this course of action at all.

For one-off "projects" - get yourself a active crossover kit with instructions on how to tailor parameters. Then muck about to your heart's content."

In answer to the question, it is set up to split the signal at whatever points are desired. But it is not just frequency: the signal is not an abrupt cutoff, as in 100% up(down) to that frequency then zero 1Hz past, but a roll-off that typically may be 6dB, 12, 24 or the highest I’ve come across 48dB roll-off per octave past the set frequency. Each possibility has pros and cons depending on the drivers, the speaker design, and in the case of analog circuits, the effect of the choice on the phase of the signal (unless the circuit includes separate phase compensation). The crossover must also balance the relative levels of each driver, and might include other features. 

As AM’s post indicates, in the case of Snaxo, that is done in-house by Naim and IIUC is not user adjustable. So, where they have predetermined particular speakers to support, they will have set up the appropriate parameters. If they do undertake custom modifications, where that is simply different crossover frequencies and adjustment of levels, it is likely an easy task - but only if the relevant information is available so they no what to set. However, any desire to alter phase setup, or frequency slopes, may represent a much higher level of customisation and cost if offered - and if even possible with the circuit design.

Against that, there are active crossovers that are customisable by the user - digital ones far more customisable than the analog type. Of course, to use them you need to know what you’re trying to set up, and measurement capability is necessary at least to set relative levels and phase.

I have an old ATC EC23 analog unit that I picked up secondhand. It can be used 2 or 3 way, crossover frequencies can be changed with 4 plug-in banks of resistors, either by requesting the appropriate ones from ATC, or it is easy to make up your own if you can solder, however the slopes are fixed at 24dB/octave. It also has adjustments for level and relative phase of each frequency band of each channel.

I also have a Behringer DCX2496, which allows ‘dialling up’ of whatever crossover frequencies are wanted, their slopes individually are selectable, likewise even the ‘shape’ of the slope, as well as setting of levels and phase. It also has some additional DSP capability, e.g to tweak the shape of the frequency response, to equalise oddities in individual speaker drivers. 

Innocent Bystander posted:

 

As AM’s post indicates, in the case of Snaxo, that is done in-house by Naim and IIUC is not user adjustable.

Correct. The only potentially user-adjustable items are the levels for each driver. These are initially set by Naim and are generally pretty good out of the box. However, with care, they can be fine-tuned to suit your particular installation. Unless you're prepared to delve into your SNAXO with the lid off, best left alone. I tweaked mine with the help of my friend Darke Bear, but if you search previous posts there are some very good instructions for setting up a 242 SNAXO written by Julian H.