Moving the frame of the question: the Chuul makes a single action Multiattack, the tentacle use is part of that action.
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From the [Sage Advice Compendium V.2.3][1] (11):

> **Is the grappling rule in the *Player’s Handbook* usable by a handless creature?**  
The grappling rule (*PH*, 195) was written for a
> grappler with at least one hand, but a DM can easily adapt the rule
> for a handless creature that has a bite or an appendage, such as a
> tentacle, that could reasonably seize someone. A wolf, for example,
> could plausibly try to seize a person with its bite, and the animal
> wouldn’t be able to use its bite attack as long as it held onto the
> person. Keep in mind that the grappling rule in the *Player’s
> Handbook* requires the Attack action, so a creature must take that
> action—rather than Multiattack or another action in the creature’s
> stat block—when it uses that rule. A monster, such as a roper, that
> has a special grappling attack doesn’t follow that rule when using its
> special attack.

The special grappling attack of the Chuul is the *Multiattack* with pincers and its tentacles. If the condition is met it does not have to spend an extra action. It does not follow the PHB's grappling rules.


> **Multiattack**. The chuul makes two pincer attacks. If the chuul is grappling a creature, the chuul can also use its tentacles once.



The creature can choose to use its tentacle because it has a valid target at that point and the condition is met. The *Multiattack* is a single action.

Also see MM (10) on **Actions**, more specifically MM (11) on **Multiattack** and **Grapple Rules for Monsters**.


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We also have some insight into design intent, albeit unofficial, in [this tweet sequence and in particular the answer by Jermy Crawford][2].

Who says:

> The DM decides the order of a creature's attacks using Multiattack,
> unless the creature's stat block mandates a particular order.


  [1]: https://media.wizards.com/2019/dnd/downloads/SA-Compendium.pdf
  [2]: https://www.sageadvice.eu/2017/06/17/when-a-creature-multiattacks-does-it-choose-the-order/