Death burst applies… somewhere.
The rules on hit points in the Monster Manual (p. 7) and Basic Rules state:
A monster usually dies or is destroyed when it drops to 0 hit points.
The conjure minor elementals spell description states:
An elemental summoned by this spell disappears when it drops to 0 hit points or when the spell ends.
This is more specific than the Monster Manual ruling, but doesn’t state that the creature doesn’t die (or get destroyed). So because neither precludes the other, they both happen, but the order is not clear, since they both happen on the same “trigger”.
On page 77 of Xanathar’s Guide to Everything, the section entitled “Simultaneous Effects” states:
In rare cases, effects can happen at the same time, especially at the start or end of a creature’s turn. If two or more things happen at the same time on a character or monster’s turn, the person at the game table – whether player or DM – who controls that creature decides the order in which those things happen.
So the person controlling the creature on whose turn the steam mephits get destroyed determines the ordering of the interaction. This might result in incentivizing the summoner to “pop” his own monsters if he fears they’ll be destroyed the next round, to get their death effect.