[RPG] When does a warlock’s familiar make their attack if the warlock has the Investment of the Chain Master eldritch invocation

action-economydnd-5efamiliarssummoning

So, Tasha's Cauldron of Everything introduces a lot of new "pet" mechanics in DnD 5e. An emerging trend for some of them is that the master can take a bonus action to command the pet to take a specific action. For example:

Circle of Wildfire Druid's Wildfire Spirit

In combat, the spirit shares your initiative count, but it takes its turn immediately after yours. The only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it to take another action.

Beast Master Ranger's Primal Companion

In combat, the beast acts during your turn. It can move and use its reaction on its own, but the only action it takes is the Dodge action, unless you take a bonus action on your turn to command it to take another action.

A Pact of the Chain Warlock with the Investment of the Chain Master eldritch invocation

When you cast Find Familiar, you infuse the summoned familiar with a measure of your eldritch power, granting the creature the following benefits:

  • […]
  • As a bonus action, you can command the familiar to take the
    Attack action.
  • […]

While it probably won't matter much for the Wildfire Spirit or the Primal Companion since they both take their turns on or right after the master, a familiar has its own initiative and acts on it own turn. So, if a Pact of the Chain warlock with the Investment of the Chain Master eldritch invocation uses its bonus action to command their familiar to take the Attack action, when does said familiar actually take the Attack action?
Contrast this with the base Pact of the Chain feature, where a familiar can use its reaction to take the Attack action on the master's turn, should the master forgoes one of their attacks:

Pact of the Chain

Additionally, when you take the Attack action, you can forgo one of your own attacks to allow your familiar to use its reaction to make one attack of its own.

Best Answer

It attacks on its turn.

Investment of the Chain Master says:

As a bonus action, you can command the familiar to take the Attack action.

The combat rules state:

On your turn, you can move a distance up to your speed and take one action. You decide whether to move first or take your action first.

Actions happen when it is your turn. When you are acting on someone else's turn, it uses your reaction:

Certain special abilities, spells, and situations allow you to take a special action called a reaction. A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else's. The opportunity attack, described later in this chapter, is the most common type of reaction.

So when you use your bonus action to command the familiar, you are commanding it to take the Attack action, and the familiar taking the Attack action is something that can only happen on the familiar's turn.

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