WebSphere Web Container uses a Thread Pool for all the requests.
For any request (doesn't matter who made it) a thread is obtained from the pool, the request is processed, and the thread goes back to the pool.
Even if the requests are one after the other, there is no guarantee the same thread will process them.
If you see one request interfere with another it is most likely something you do in your code and not due to how WebSphere behaves.