Yes, it does matter. You need a vapor barrier under the siding. You can use a house wrap like Typar, Tyvek, (they are all about the same.), or styrofoam insulation will work as well.
If you have not paid him yet, DON'T !
If you have, you will probably have to take him to court to get the money to have the job done right.
He either does not know how to do this right or worse, is just skimping.
You probably had to get a building permit so, I would talk to the inspector and see how knowlegeble he/she is on this subject.
Get it fixed.
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