It's possible that the fusion bath is enough to trigger the "antimatter generation" that you mention?
My idea is that once you channel the ionized fusion plasma through the dilithium crystals you integrate
the exotic energy output you get (is that why they refer to a "matter-antimatter integrator"?) into the matter-antimatter annihilation plasma stream to get as a final result (intermix) the exotic energy you need for warp drive and - to some extent - creation of new antimatter.
Certainly the link between dilithium and antimatter is evident from The Alternative Factor, although what that link is was of course never clearly defined.
When the phenomenom happened first, they were able to measure a "drain" on the crystals, hence Kirk ordered Lt. Masters to immediately "re-amplify" these.
Later they used this "drain" to pinpoint the source of the space anomaly (i.e. used the crystals as a sensor) and Kirk ordered Lt. Masters to set up the experimentation chamber.
I don't really know what the screenplay writer had in mind.
Maybe he felt that if the crystals would have an amplifying effect to influence the fabric of normal space, then antimatter space would have a de-amplifying effect on the crystals.
I do think that the popular TNG setup (matter at the top, antimatter at the bottom, anihilation takes place via a crystal in the centre) is probably a gross simplification of what actually occurs - and luckily, no onscreen dialogue ever says otherwise. So, what else could be happenning then? A miniaturised version of the TOS dilithium assembly is an attractive possiblity, at least.
I found one comment from the ENT protagonist Tucker in "In A Mirror, Darkly" (or was he rather an antagonist in this episode?
) extremely illustrative:
Aboard the USS Defiant
(NCC-1764) he said he felt like a "steamboat mechanic" who suddenly has to understand the mechanics of the first "interplanetary spacecraft". We are looking at a time difference between TOS and TNG of close to a 100 years.
In-universe I'd expect that the matter-antimatter propulsion concepts have evolved and what we've seen in TNG (or its era) is possibly a great leap forward - or just a very small step if already the Enterprise
had such a TNG warp core in ST VI.