The familiar attacks immediately, consuming your bonus action.
The text for this Boon says simply:
As a bonus action, you can command your familiar to make one attack.
There is no mention of a delay, nor an additonal cost to the familiar, therefore there isn't one.
For comparison see the Ranger Revised's beast companion (also Unearthed Arcana):
The 5th level ability Coordinated Attack states:
When you use the Attack action on your turn, if your companion can see you, it can use its reaction to make a melee attack.
In contrast to the Warlock's familiar, the beast companion has to use its reaction to make the attack, and so that is clearly spelt out.
As an aside, if you're worried about balance, if anything, the Ranger's is the more powerful action - it's likely that your PC's bonus-action (the cost the warlock pays) will be more valuable to you than your beast companion's reaction (the cost the Ranger pays). However the Ranger does also have to pay the opportunity cost of needing to take the attack action themselves - whereas the Warlock doesn't need to do anything to trigger this use of their bonus action.
That said, both of these optons are unearthed arcana, and thus playtest material, and so may well be unbalanced when compared to official published game materials.