You have to use type: announce with any media player entity that alexa considers a speaker group, including media_player.everywhere. Using type: tts will not work.
Notification Component - Functionality
If you do not want to the announcement sound, you can use type: tts with a list of media_player entities:
service: notify.alexa_media
data:
message: This is my message
data:
type: tts
target:
- media_player.1
- media_player.2
- media_player.3