Key Generation for TOTP in TLS
You seem to be confusing a few things here, mainly OTP schemes and TLS.
There really is no strong relation between the two, except for maybe the case that more often than not, you use OTP schemes over TLS.



The IBM Knowledge Center links makes a reference to the pre-master secret which is encrypted using the server's public key and then used (along with client's and server's nonces) to derive the actual master secret in TLS.



In OTP schemes, the shared secret is usually generated at random with the appropriate length and then encoded for better handling.



With common RSA connections, the server doesn't actually look at the pre-master secret and just takes what you give him. More often than not, he doesn't care what it actually is.



The fact that the OTPauth string was encrypted using the server's key was probably meant as a security measure to enforce access to the server's private key to be able to give out / verify OTPs. Or it may indeed as suggested be an try to let the client pick the shared OTP secret so not all clients are screwed in case of a partial leak of the secrets.



The numbers before the secret should encode usage parameters and / or give the secret a name for further processing.