Just to understand your question, you are asking on how CLM stack connects to the provisioned VM, hosted/provisioned in Public Cloud? e.g: AWS or Azure.
Let me know if my understanding is correct.
To manage a vm, hosted in public cloud, we provide an option to customer to configure a compute provider so that any provisioned VM in public cloud gets enroll in BSA (BMC Server Automation) and with that, we can manage the server as it install the RSCD agent on targets to communicate.
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Do you mean how does the end user login to the provisioned server on the Public Cloud capability (AWS, Azure etc)?
Generally the client would have a specific VPN type tunnel to the Public Cloud Provider and then in theory the IP Address of the server on the Public Cloud environment would be accessed as if it was on the internal LAN. THen ou can use SSH/RDP as normal.
Doing this means that the Public Cloud becomes an extension of the internal network.