I can't speak to arborvitae, but some trees and shrubs like red cedar & yaupon holly will not grow new growth from limbs that have been cut too far back.
The way that I understand Lucy's post... You now have exposed trunks, those limbs will probably die back... Maybe you get new limbs from the trunks... Maybe not.
For future reference, In Georgia, we trim in February, Just before the trees and bushes come out of winter dormancy.
The main reason for late winter pruning rather than autumn is so we don't have to live with the unsightly pruning cuts all winter... the trees and bushes immediately start sending out new growth.
Another reason for avoiding autumn pruning... The plants have just enough time to send out new tender growth... which always gets damaged by the cold.
It's unfortunate that your gardener failed to inform you of this information.
