No. The buttons open X in a new tab. You post, follow or write there, from your own X account. The app never does it for you.
What readers see
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Select a button on the Confluence page.
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Confirm that you want to open X in a new tab.
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Sign in to X if asked. Then check what X shows and finish it.
Some buttons fill in text for you. You can review it before you post. X lets each account choose who can message it. A Hashtag button opens a new post. It does not show a list of posts with that hashtag.
For all 5 buttons and their settings, see Embeds and buttons. To ask a private question, choose Message Button. Check who the account lets send it messages on X.