When mounted you have two options. Control the mount (if it will let you) or allow it to act independently.
If controlled, the following applies:
The initiative of a controlled mount changes to match yours when you mount it. It moves
as you direct it, and it has only three action options: Dash,
Disengage, and Dodge.
This restriction applies to actions not reactions. Therefore it may take the reaction described in "Coordinated Attack " and attack:
Beginning at 5th level, 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 against any creature within range.
If acting independently then:
A controlled mount can move and act even on the
turn that you mount it. An independent mount retains its place in the
initiative order. Bearing a rider puts no restrictions on the actions
the mount can take, and it moves and acts as it wishes.
Since there are no restrictions, it may make the reactionary attack in this scenario also.