Anywhere we can add a Tag, and while adding or editing a new Tag, clicking on "Manage standard tags" redirect current page to the Tags managing page, while discarding the current tag(s) that were added.

The browser does not seem to sense that a new tag was added as it is not using a regular INPUT html element, in which, it will display a "Are you sure..." dialogue that will prevent the user from losing it's data (tag/s).

Even so, considering the browser is able to detect new data input, it seems to me that from UX perspective, it is better to open the tag management page in a new window, as it will prevent the current user from losing its navigation and newly added tag(s) and/or other data added or updated in the form.
(Reminds me similar UX issue with the RSS block - MDL-26675)