The concept is quite simple, but the process of matching is not so simple in that it involves carefully carving out the backside of the FB, removing wood from the neck or scroll, or adding weight somehow. The idea is to get vibrating parts of the instrument to create constructive interference wave patterns instead of destructive or cancelling ones. That way the parts of the instrument are reinforcing the vibrations. The zero modes should be the lowest frequencies so that as many partials as possible are reinforced. By the time one gets into the upper range, most of the notes are a partial of the zero mode frequencies. From a purely physical standpoint, this is intuitive. In practice it is not so simple. The whole instrument has other modes and other parts that also contribute or react constructively or destructively. Even the bow has something to do with resonance.
On my instrument, straight from the maker, the A zero is a "C" resulting in such strong C's everywhere on the instrument that it is possible to get close to a reasonable tuning without a tuner. The tap tone of the fingerboard beyond the overstand sounds like it is also a "C", but a bit above the A zero mode frequency, perhaps two octaves or maybe just one depending on where you strike it with a mallet. This is not matching the B zero, but apparently some makers are tuning parts of the instrument in the building process. Clearly, all the harmonics of the low C, the G's, F's, etc. also are easy to find because they are louder when in tune. On my instrument, this was one of the first things I noticed about it even with the factory set-up, which I improved upon in several ways to fit my playing style. When I dressed the FB, I was careful to take off as little wood as possible to get the job done, and I removed nothing beyond the overstand. I really didn't want to change what the maker had intended. I kept the shavings and these together were very light in weight;- certainly far less than a gram. I don't know if this helped, but the dressing of the board really surprised me in that all the notes everywhere sounded better afterwards. These details gave me a good deal of respect for the makers at Kremona, even if the wood they use for the DB's is not the fanciest, the instrument's characteristics overall suggest a good bit of care went into the dimensioning and design, which is Rubner influenced. As the instrument has opened up, it just gets more and more responsive, to the extent that band mates that remember when it was new comment from time to time. I don't think that resonance matching alone makes or breaks the performance of an instrument, but a great set-up is the combination of a lot of small details adding up, and this can be a boost for some instruments. It didn't surprise me much that small production shops working in the ancient guild tradition pay close attention to the cavity resonance. Like I said, tuning the wood is intuitive, even if one just does it out of instinct and not out of scientific study. It is plausible that the practice predates Hutchins' findings by a couple of centuries or more.
I would go further to point out the partial series of the low BB string resonate in a complementary way to the "C" and tend to balance the response of the instrument as does the E string and A string and other open strings. An instrument built on the foundation of a low C cavity resonance makes sense intuitively.
Balance is the tricky part. Getting an instrument to sound good throughout the range is indeed an art that goes well beyond the science that describes the process. Those that did this without technology that we currently have are the equivalent of Einsteins in my view. Today, I don't think luthierie is what is was in Stradivari's day. The Renaissance makers were breaking new ground.
Mersenne had just uncovered the relationships underlying string behavior by studying visible waves in strings (ropes if you please) that were tens of meters in length. By studying in the macroscopic end of the spectrum he was able to establish a foundation for wave behavior that is observed throughout the sound spectrum. Recently it has been observed that harmonic resonance is also involved in the stability of atomic structure. Indeed, it may be the glue of the universe. It is not surprising to note that Mersenne was a contemporary of Amati, and that soon afterwards Stradivari was able to build the quintessential violin. These men were definitely paying attention to the math, though they may not have recognized it as either math or science in the way the modern world views these disciplines. While the word science derives from the ancient latin word for knowledge, Renaissance "scientists" were regarded as "Natural philosophers". They were concerned with the relations of natural phenomena.
Hutchins' work and that of other investigators tends to quantify what was done by these makers and apply it to modern instrument making. Hers was careful detective work over a lifetime of dedication to the concept that there are specific measurable physical relations underlying the making of fine acoustic stringed instruments.