I have a Web API Controller with the following method inside:
public string Tester()
What you describe matches the default behavior of the ASP.NET Session State and can be solved by disabling it in web.config.
Access to ASP.NET session state is exclusive per session, which means that if two different users make concurrent requests, access to each separate session is granted concurrently. However, if two concurrent requests are made for the same session (by using the same SessionID value), the first request gets exclusive access to the session information. The second request executes only after the first request is finished. (The second session can also get access if the exclusive lock on the information is freed because the first request exceeds the lock time-out.) If the EnableSessionState value in the @ Page directive is set to ReadOnly, a request for the read-only session information does not result in an exclusive lock on the session data. However, read-only requests for session data might still have to wait for a lock set by a read-write request for session data to clear.
Source: ASP.NET Session State Overview