The transmitter operates on a “first come, first served” basis. So the first client to transmit gets control of the transmitter until they un-key. When your client is transmitting, you will see the familiar TX indicator in the lower right on SmartSDR for Windows. When a client other than your own is transmitting, an indicator such as the one shown in the screenshot below with inverted colors will be show to draw attention to the fact that the radio is in transmit mode by another client. You can hover over the indicator to get information about which Station is transmitting.
It looks like this when your client is transmitting:
It looks like this when a different client is transmitting: