What to do with Escrow Refund

Long story short, we refinanced our home (California if it matters) with a different lender. The new lender told us the previous lender should be refunding us the money in our escrow account. I asked if we needed to remit those funds to them (new lender) to fund the escrow account. He said we did not need to since they would be setting up a new account and would be responsible for paying our property taxes and homeowners insurance. Otherwise, the escrow money will go towards paying off some credit cards and towards savings.

What should I expect to happen?