A good question!
Actually, it took me some time to understand, so it definitely needs some explanation.
First, upon using an impedance adapter, the volume is expected/implied to be matched to the same levels for proper comparisons.
Second, the primary purpose of impedance adapters is to better match a source and a transducer. A most common case is for a too powerful source that can deliver only few % of its power before making a transducer sound too loud, often with some background noise. In this case, a proper impedance adapter can dissipate some energy, so the source will be used at its higher (more optimal) power levels, often with less noise. (Again, volume matching is assumed).
An important point from here is that using impedance adapters implies having strong sources that can provide more power. Weaker sources, like phones, may not have sufficient driving voltage when used with impedance adapters.
Now, the third and most relevant to your question point, which I actually missed before, is that using impedance adapters may strongly affect power distribution to different drivers for multi-driver IEMs. Taking AST as an example, the bass BA takes most of the power in the AST crossover design, leaving less power for multiple treble drivers. As a result, AST sound bass heavy (too much for many) and somewhat gentle/anemic in treble (definitely too gentle for me). Using an impedance adapter with AST makes power distribution more even (more story to it, just not to be overly long). As a result, bass BA gets less power and treble BAs more with the great overall effect (to my ears, at least).
Now a bit of the background, the effect of the impedance adapters was brought to HIFiers' attention with KZ AS16 pro, where KZ admitted using wrong source setting of 18 Ohm for the source impedance, while tuning (they dialed the IEM impedance of 18 Ohm instead). So 18 Ohm impedance adapter should bring an original tuning (that is noticeably leaner (less bass, more treble again) and closer to original AS16; I like both versions). KZ actually promised to produce a properly tuned version of AS16 pro, but it did not materialize, likely because the "wrong tuning" actually worked out well, if not better, for most.
After learning from AS16 pro, I decided to test other all-BA KZs, and AST seem to be a similar case, as I described above. Given AST impedance of 30 Ohm, 25-40 Ohm adapters make the bass leaner, and treble more pronounced.
Also TRI Clarion tips are great for AST.
@cqtek and
@paulwasabii may chime more on this, from them I learned most what I summarized above, my big thanks!
I miss Master Slater so much! Under his patience quidance, I started some simple moding to enjoy this hobby. He would be a really great person to contribute here with more insight and his great explanations.
Great and very timely mods now that KZ may feel to make KZ PR1 less relevant by the Pro version.
I will definitely try what I can do along your lines after I get my Pro (it is in a local post office since Friday, Canada Post do not do weekends...)