Is it normal to have bruising after a facial fat transfer?

Yes. Bruising can and will occur anywhere there is trauma to the body. Introducing needles and cannulas to the face to inject fat can certainly cause bruising.
Yes. Injections of fat or fillers commonly cause bruising. It will resolve.
Yes. Icing the area before and after can help minimize the swelling and brusing but most people will have some.
Fat Grafting. Some bruising after fat transfer may be normal. Be sure to follow the instructtions of your plastic surgeon carefully including taking a homeopathic remedy to reduce bruising and swelling. The results of fat grafting can be permanent, beautiful and natural-looking.
Not preventable . Your anti inflammatories may increase the tendency for bruising. Use of arnica (pills and cream), bromelain, ice compresses, head elevation, and excellent minimally traumatic techniques may minimize but not always prevent bruising.