Dedicated email to register on exchanges right? But still the information can be leaked from exchange or sold by exchange itself since it happened in the past so use email in your primary mobile and the authenticator on separate mobile better consider using Authy which is better than Google Authenticator.
No one is immune from a data leak or breach on an exchange, but the less access to different sites can minimize the credentials info losses.
I don’t remember if any authenticator beside Google are offered in the exchange.