I logged out from the connection client but the Bentley's product window is still opened, so I can use that product after logging out, if I logged in to the connection client from another computer and use the Bently's product is that means that I am using 2 devices with one licenses so that I may have to pay additional fees or is that considered as a violation of using the license?
The usage is machine based. In this scenario, you will be using two licenses.
Though you are logged out of Connection Client, since the product is open, it will be running in offline mode. Next time once you log in to Connection Client in the machine, usage will be reported. Please go through the below wiki to understand how usage is calculated.
How is usage calculated? - Licensing, Cloud and Web Services Wiki - Licensing, Cloud and Web Services - Bentley Communities
but why there is no alert or warning from Bentely for such case, I am just using the product and deal with logging in and out from "connection client" considering that this is only way for the license using, I have to pay for something is not clear from Bentely
When you work in offline mode, i.e. your computer is not connected to the Internet or you are not signed in to CONNECTION Client, your machine is not communicating with the licensing server and the alerting service. This means that the system is not aware if any licenses are being consumed. If there are any licenses running - they do not contribute to the configured alert threshold, even though licenses are being used. Such usage is recorded and stored on the local machine but will be synced with the licensing server the next time the machine is connected to the Internet/you sign in to CONNECTION Client - and this is why you may unknowingly generate additional license usage.
See:
License Alerting, and Limitations of Threshold Alerting
Answer Verified By: Jacek Majda