The shutter is actually being closed. On mirrorless cameras the shutter is by default open so that viewfinder framing can be accomplished, then it quickly closes, opens for the photo, and ends closed before opening again to act as a viewfinder.
In the case of a reference photo it is closing, not opening, taking a read of the sensor, then opening again.
Older ones do, because the readout speed of sensors was not fast enough. Cameras with stacked or global shutters generally don't, because it's no longer an advantage. In between, it's a choice you can make whether or not to use the shutter.