There is linguistic precedent in the rule that the word "move" does not expressly refer to the voluntary use of one's own Speed.
Does moonbeam deal damage when you cast it? What about when its
effect moves onto a creature?
The answer to both questions is no. Here’s some elaboration on that
answer.
Some spells and other game features create an area of effect that does
something when a creature enters that area for the first time on a
turn or when a creature starts its turn in that area. The turn you
cast such a spell, you’re primarily setting up hurt for your foes on
later turns. Moonbeam, for example, creates a beam of light that can
damage a creature who enters the beam or who starts its turn in the
beam.
[...]
Reading the description of any of those spells, you might wonder
whether a creature is considered to be entering the spell’s area of
effect if the area is created on the creature’s space. And if the area
of effect can be moved—as the beam of moonbeam can—does moving it
into a creature’s space count as the creature entering the area? Our
design intent for such spells is this: a creature enters the area of
effect when the creature passes into it. Creating the area of effect
on the creature or moving it onto the creature doesn’t count. If the
creature is still in the area at the start of its turn, it is
subjected to the area’s effect.
Entering such an area of effect needn’t be voluntary, unless a spell
says otherwise. You can, therefore, hurl a creature into the area with
a spell like thunderwave. We consider that clever play, not an
imbalance, so hurl away! Keep in mind, however, that a creature is
subjected to such an area of effect only the first time it enters the
area on a turn. You can’t move a creature in and out of it to damage
it over and over again on the same turn.
In summary, a spell like moonbeam affects a creature when the
creature passes into the spell’s area of effect and when the creature
starts its turn there. You’re essentially creating a hazard on the
battlefield.
Best Answer
This spell ended up printed in Xanathar's Guide to Everything, with clarifying language.
I don't believe it was ever intended to provoke AoO.