I don't trust Authy and a discerning security professional shouldn't either. There are _a lot_ of red flags.
* First: Forcing users to download their stupid app. TOTP is a widely documented protocol. There shouldn't be a need to download a particular app unless there is an ulterior motive.
* Second: secrets are stored in the cloud. Guess what the key to access them is? An SMS. Yes those un-encrypted, un-signed, un-authenticated, spoof-able, forward-able, plain-text, non-guaranteed delivery, MITM ready, message system. Seriously?
* Third: No choice for migrating to another app. Even though Authy has access to your secrets, you cannot export them. There is an ulterior motive here. Authy does not want you leaving them and will play dirty to keep your on their platform.
* Fourth: You will get locked out of everything if Authy decides to pull the plug on you. If you get 'cancelled' for having a non-popular opinion, Authy could revoke access to every single one of your accounts.
Avoid like dysentery.