Open attached project -> 1.unity scene
or
1. Create your project
2. Create 2 script that play some short video from their Awake function
3. Assign these scripts to some objects on your scene or to the same object

4. Build&Run project on the device

Actual result:
Video of only one of these scripts is played. Video from the Start function of the other script is not played
No warnings in the log

Expected result:
All videos are played in some order

Devices:
Sony Xperia Z1, Android version 5.1.1
iPad, 2 iOS 9.2.1

Unity versions:
Version 5.3.2f1 (e87ab445ead0) - reproduced
Version 5.4.0a6 (97b6a3660dbf) - reproduced
Version 5.4.0b5 (60658ab74c44) - reproduced