I doubt that the Romulans used dilithium for their large AQS-driven Warbirds, but maybe they had a bunch of shuttles onboard that don't use AQS but a M/AM-dilithium setup?
They still use dilithium. The AQS generates the power... the dilithium is just part of the warp reaction.
As for the ships exploding vs. imploding, I have to wonder if the singularity could actually dissipate while still under containment prior to the ships destruction, perhaps as something of a failsafe to make sure that destroyed Romulan ships DON'T go around leaving rogue black holes in the event of disaster. The ship has failsafes to, at least try to, snuff out the singularity before the ship is completely lost.
EDIT
I'm envisioning a system that could potentially make Romulan ships moderately more safe than others... their version of a warp core breach would (hopefully) just be the AQS being snuffed out. The ship itself is still fine, they just... no longer have warp capability.