Assume you refinanced with your existing servicer, as escrow accounts are not transferred from servicer to servicer during a refinance. Sounds like you wanted to escrow on your new loan, since you were on the old loan. It is typically very much to borrowers' benefit to use existing escrow account money for the new escrows whenever possible, as it lowers the new loan size and reduces the cash due at closing. There is no downside to transferring escrows, assuming the old account has adequate funds in it.
You sound like you are upset about this, and I don’t understand why. The choice is a higher loan size and payment to borrow the money for the new escrow, or bringing money to closing for escrow, then waiting 30 days for an escrow refund check from the old account, versus funding the new escrow account from the one already in place. It’s far to your benefit to use the existing account, as you indicate your lender did.