So why connecting to SSH if the snapshot was already made?
That's only one connection of two that are established. The first one is not displayed in session and is used to perform AAIP (pre-freeze/post-thaw scripts, Oracle)
The only quiescence was made by the VMware Tools and scripts if configured?
If network is not available then VBR can failover to VIX mode. If network connection is available then quiscence is performed via the first ssh connection (not displayed in session).
SSH connexion does nothing to do a better consistence, correct ?
The connection that you can see in session is done to perform indexing and/or collecting data about filesystems' mount points (used for FLR).