This was caused by the local Default-568h@2x.png file (which is required by iTunes Connect).
When I removed the localization from the file, it started working fine in iOS9.
This does not help anyone whose application is currently in storage with a localized default saver file of 568h @ 2x.
As far as I can judge about this, you need to have a .xib file "Splash Screen" defined in the settings of your project (then you lose autoscaling for iPhone 6 and 6+, which is ideal for our application).
Apple . , , iOS9 ( ), , () .