No, you are confusing "wallet" with "address". A wallet is little more than a seed for an RNG and a log of transactions. Every new transaction starts with a source address and results in two destination addresses: the primary destination (payee) address and the address where the remainder of the source balance goes. You definitely want to maintain control of your change, so your wallet uses the seed to deterministically generate a keypair for a new address and that is where your change gets sent.

I've got no interest in digging into their methodology, but feel pretty comfortable assuming that they've grossly misrepresented all of the above as "accounts".