I cannot know for sure what the Kepware message "Active connections still exist." refers to, but you are right, it probably refers to an reference to an OPCServer object (in OPC Classic) or an OPC UA Session, which are "global" connections, not to a tag. The other (less likely) explanation is that it refers to an OPCItem (in OPC Classic), or an OPC UA monitored item.
If you subscribe (I guess that's what you call "listen to") an item/monitored item ("tag"), our software will attempt to remain connected until you explicitly unsubscribe using one of ther UnsubscribeXXXX methods.
If you do one-time operations such as ReadXXXX, WriteXXXX, we will connect and then remain connected for a "hold period", then disconnect unless there is another request or a subscription (see above).
Therefore if you are no longer calling operations such as OPC reads and writes, AND you have explicitly unsubscribed from the subscriptions you have made, you should see that after the hold period elapses, our client (you application) disconnects from the target OPC server.
If this is not what you observe, pls provide a way to reproduce the issue.
The default hold periods differ between OPC Classic and OPC UA and depend on the operation(s) performed, but do not exceed 60 seconds total in version 5.32. Earlier versions might have somewhat different defaults.