Manual announcements are sent to all devices mainly because Alexa doesn't ask which devices you want to announce to.
When you set up a routine to do announcements, there is a screen where you can specify which devices. If you just installed your firestick, it is probably not selected as an announcement device in your routine. Edit your routine and take a look at what devices are selected for announcements. It is under Actions, tap the line that says "Announce xxxxxxxx", tap next, and you'll see a list of the devices.