The reaction would not go off
The general rule, from page 252 of the DMG is as follows:
If a reaction has no timing specified, or the timing is unclear, the reaction occurs after its trigger finishes, as in the Ready action.
A similar rule is in Xanathar's Guide to Everything:
the reaction happens after its trigger completes, unless the
description of the reaction explicitly says otherwise.
The trigger, in this case, is the orthon dropping below 16HP. If it drops to 0HP, it immediately falls unconscious. The unconscious condition includes the incapacitated condition, which in turn includes an inability to take reactions. Therefore, when the trigger is finished, the orthon no longer has the ablity to use its reaction.
Note that the above rule is specifically invoked in case of an unspecified and/or unclear timing. I certainly think this is the case.
Perhaps Explosive Retribution makes more sense as an innate ability, such that a sufficiently damaged orthon automatically explodes, in which case dropping it to 0HP would not prevent the ability from triggering. However, RAW it is listed as a reaction.
Therefore, I would consider an exploding 0HP orthon to be a deviation from RAW, but not necessarily a bad one.