The obvious things would be scale ranges and sublayer visibility, but because you said you can see the layers if added directly as feature layers, and also in the Legend, I think it's unlikely to be either of these. (However, worth checking the in the Layer Details to see if all of these sublayers are actually turned on - go to the Layer Details like before, and then you should see the sublayers all listed in this panel - are there any checkboxes that are unchecked? The sublayer visibility should be respecting what's in the rest endpoint - e.g. same as the 'Default Visibility' attribute on the sublayer on the rest endpoint.) I guess one other thing is to make sure the layers have finished downloading - has the status bar at the bottom of the map definately completed?
Is your server public? If so, I could take a look directly and try to reproduce what you're seeing.