You are on a post or a page. You click the WHT.day icon, or use the shortcut, and that item is saved to your account: the URL, the title, and the readable text, with images when the page has them. For an X post, the saved record is the post itself — text, author, images — not a thumbnail that depends on the link staying up.
It acts when you ask. The privacy policy is specific about this: page contents are read after you choose Save, a shortcut or a context-menu command, not as you browse. There is no background import of your X bookmark list.