Thank you for your post. Glad to hear you are making good use of the AUX port by using an Echo Dot! Alexa won't be able to turn on the Wave Music System IV, so we should disable the auto-off feature. This won't hurt the system but could cause the system to consume a bit more power (the auto-off feature is there to help conserve energy).
Here are the instructions:
Press and hold Alarm Setup (Menu) until -SETUP MENU- is displayed
Press Tune/MP3 > nine times until AUTO OFF- is displayed
Press Time – or Time + to select NO or YES
Press Alarm Setup (Menu) to exit the setup menu or wait 10 seconds for the setup menu to exit automatically