Is there any way I can know how my add-on card is being utilised?

Yes, you can know how your add-on card is being utilised.

As an add-on card is a supplementary or secondary card, the primary card holder can track the withdrawals and purchases made by the add-on credit card holder.

In fact, it is recommended that you monitor the expenses being made on the add-on card, because at the end of the day, the add-on card will have an impact on your credit score.