Read your contract again and make sure it reads, "Replace soffit and fascia" not "Cover soffit and fascia" before you and talk to the owner of the company.
If the word is "replace":
Does it say with what?
Tell him/her that you are not giving them one more cent until they remove what they have done and follow the contract. (I hope you are not into him for too much!)
You never cover rot!
Contact the Building Inspector, and if a permit was required, have them chime in on normal construction practices.
NOTE* This is why it is good to get permits!!!!
Take photos of what they have done. (you may need them in court)
If I were hired to do a job like you have described, I would have removed the soffit and fascia and installed new fascia boards. They would not have to be finish boards because they would be coverd with aluminum. I would install a nailer under the soffit and use vented, vinyl soffit panels. You would know this because it would all be in the contract.
Now, let's say your old soffit was in good shape. I would use atleast a 4" hole saw and drill a hole between every rafter.
If your contract reads "Cover":
You are out of luck! But, I would still talk with the owner to see if you can change the job. (It will cost you more but, you will get a better job!)