Of cause the sizes are different. It depends on the beam span, the slab thickness, service loadings, etc.

Foundation is not straight forward. But then again, extension is not a massive job.

I have seen entire extension teared off from the main building slanting & also extension sink.

Size of the footing depends on the depth of the footing too. There are just too many things you need to know before you decide on footing size.

Unless the contractor gives you 5 years warranty, else I won't follow their advise. You have to understand, once the drawings are stamped by engineer, it's at least 50 years warranty.

Your choice.