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No. When you add something like the PTR, it'll make a completely separate service that will appear in the manage tags dialog as a second tab. PTR tags will stay in one list, your 'my tags' will stay in another. Any time you choose to edit tags, or to parse them from something like a booru download, you will be choosing which tag 'domain' they will go to.
Normally when you search on search pages, you will see the tag domain is 'all known tags'. This is essentially a union of all your tag services, which for you at the moment is just 'my tags'. It'll be 'my tags' and the PTR if you add the PTR.
The only way the tags you have added to 'my tags' can be moved to the PTR is if you specifically choose to. You might copy them from the 'my tags' page and paste them to the PTR's, or you might do a larger migration using services->tag migration. If set up to sync with the PTR and touch nothing, no privacy violation will occur. You can't really make a 'mistake' here unless you are specifically reckless, you have to choose everything.
The 'commit' part is a special part of sending tags to the PTR. Rather than upload immediately, when you add them to the manage tags dialog, they are instead in a local-only 'pending' mode. This lets you edit them if you like before you commit by uploading them to the server. When you have pending tags, you will get a new 'pending (count)' menu in your main gui's menubar that lets you send them all up in one go when you are ready. This is the only way that tags can ever be uploaded to the public space--you control it completely.
If you do wish, you do not ever have to pend a tag to the PTR, and can use it exclusively in a read-only way.
If you want to get a feel for multiple tag services, try going into services->manage services and adding a new 'local tag service'. Call it 'clothing' or something and experiment with the new 'clothing' page you have anywhere you edit tags.
Let me know if there is anything still confusing. Thank you for your feedback, I will improve that help.