From the Sage Advice Compendium V.2.3 (11):
The DM decides the order of a creature's attacks using Multiattack,
unless the creature's stat block mandates a particular order.
This ruling is supported by Simultaneous Effects (XGtE, chapter 2)
Most effects in the game happen in succession, following an order set
by the rules or the DM. 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. For
example, if two effects occur at the end of a player character’s turn,
the player decides which of the two effects happens first.
So what are effects?
DMG errata version 2.0 page 1:
Combining Game Effects (p. 252). This is a new subsection at the end
of the “Combat” section:
Different game features can affect a target at the same time. But when
two or more game features have the same name, only the effects of one
of them—the most potent one—apply while the durations of the effects
overlap. For example, if a target is ignited by a fire elemental’s
Fire Form trait, the ongoing fire damage doesn’t increase if the
burning target is subjected to that trait again. Game features include
spells, class features, feats, racial traits, monster abilities, and
magic items. See the related rule in the “Combining Magical Effects”
section of chapter 10 in the Player’s Handbook.
So we can savely gather that monster abilities are indeed effects and that either way the controller of the creature decides the order of the effect. In this case, it is most likely the DM who may choose either way.
