With the VM running, try looking at the VMs USB & Bluetooth settings, either from the VM's settings or the Fusion menu bar Virtual Machines > USB & Bluetooth. See if the USB stick connected to the Mac is listed. If it is, select to connect it to the VM.
You may also want to check the VM's USB & Bluetooth settings while the VM is running. See if the settings say to connect the USB stick to the Mac, to Windows, or to ask what to do. The device may be set by default to connect to the Mac - which would explain why you do not see it asking where to connect the device.