Objects do not trigger Opportunity Attacks
Your assessment is correct. The rules for OA state that (emphasis mine):
You can make an opportunity attack when a hostile creature that you can see moves out of your reach.
As you can see the rules are very clear. Unless something is a creature it can't provoke an OA.
Further, the turret created by the artillerist is not a creature but an object. From the UA:
The turret is a magical object that occupies its space and that has crablike legs
Thus, the turret also can't provoke an Opportunity Attack.
It may seem reasonable for a DM to want to change the Artificer turret to a creature (likely a construct is appropriate). However, do keep in mind that this changes a lot more than just Opportunity Attacks. There are a number of spells and abilities that can only affect either creatures or objects or work differently with them.
With the release of Eberron: Rising from the Last War nothing changes
This question was asked about a playtest UA version of the Artificer which has now been officially released in Eberron: Rising from the Last War. The wording of the artillerist turret has changed, it is called an eldritch cannon now. However, it is still an object:
The cannon is a magical object.
Therefore, this version of the artillerist cannon also does not provoke Opportunity Attacks, as explained previously in this answer.