Yes, to mirror or cast content to an Amazon Fire TV Stick, you need both the Fire TV Stick and the device you are casting from (such as a phone, tablet, or laptop) to be connected to the same Wi-Fi network. The Wi-Fi connection is necessary for communication between the devices and to ensure a smooth streaming experience.
When you cast or mirror content to the Fire TV Stick, the content is transmitted wirelessly over the local Wi-Fi network from your casting device to the Fire TV Stick. This allows you to see the content from your phone, tablet, or laptop on your TV screen.
Without an active Wi-Fi connection, you won’t be able to establish a connection between your casting device and the Fire TV Stick, and therefore, you won’t be able to mirror or cast content to the device. Both the Fire TV Stick and the casting device need to be on the same Wi-Fi network for the casting process to work.