The impression I get is that aether weapons are never matter conversion or disintegration beams. They don't work by breaking things down in a subtle, nucleonic or molecular level, they do it relatively conventionally, by heating things up until they denature the old-fashioned way, the same as nuclear and antimatter weapons, lasers, or just plain old fire.
The difference is in the way the energy from the aether is conveyed. Sometimes it's indirect and relatively conventional; it's conveyed by photons, protons, and/or neutrons. This includes 'aether energy weapons'. For 'aether shock weapons', though, the target is exposed to the aether directly, which means the energy is conveyed by more exotic means, which might include a mix of normal particles with their antimatter equivalents, or more exotic particles that I don't really know about but am pretty sure I wouldn't want to be immersed in.
If they work this way, they don't eat matter, they just burn it or blow it up... though for an unshielded target shot by an aether shock array it'd be hard to tell the difference unless you had some way to count the particles left over after it was atomized.
I think there's a lot of other ways to explain the effects, (anti-)particle beams and pulse lasers can already produce some less than intuitive results, since most people's 'intuition' treats all directed energy weapons like beam lasers, in much the same way most peoples' understanding of animal behavior is based on dogs.