This is common. There's nothing strange or sketchy about it. A consultancy (or recruiting agency) found you and presented you to this employer. The employer decided to hire you and gave you a job offer.
Your employer will, very likely, pay a fee to the consultancy when you begin working. But that is between them. You don't need to do anything at all about that.
Another person might send their resume directly to the employer and be hired. In that case the employer (usually) owes no fee to any agency.
You should be sure of this, however. If you haven't already done so, read the offer letter carefully. It says, clearly, who will hire you.