This plugin looks about right, free too. Right now you can't be specific (their roadmap says they should allow group seletion at some point) but if the users dont have "Can work on Issue" permissions they can't see the work logged.
You are very welcome. :)
For the follow up, I suppose I would leave that to the notification scheme. Seems most simple. Ensure that the Customer User isn't in the various time-logging related events:
I would think.
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