The Chrome extension has two kinds of settings: ones inside the extension on LinkedIn, and ones inside Stardex.
By default, Stardex opens on LinkedIn. You can turn that off in the extension, not in Stardex Settings.
Find the gear on the extension, and turn off the setting. This is per user.

Chrome extension gear for auto-open
You can also install (or confirm install) from Settings → My Settings → Browser Extension: stardex.com/settings?tab=my-settings§ion=browser-extension
If it is already detected, you will see Extension installed. Otherwise there is an install button to the Chrome Web Store.

Browser Extension install and toggles
If you do not want Stardex to click through a LinkedIn profile to capture more than the top of the page, turn on Disable extension auto-clicking.
This lives in Settings → My Settings → Browser Extension. If the toggle is locked, an admin has turned auto-clicking off for the whole workspace under Settings → Organization → Compliance → Chrome Extension Settings: stardex.com/settings?tab=organization§ion=compliance

Org Compliance Chrome Extension Settings
When auto-clicking is off, only the top of the experience is stored.
If you do not want the extension to auto-sync LinkedIn inbox messages into Stardex, turn on Disable message sync on the same Browser Extension page.