It may be that the display assembly isn't seated correctly. Try following the display assembly replacement walkthrough up to step 11 and reseating the tabs located at the top of the device. Be careful when closing the device, as trying to force the display together against resistance may cause damage to the LCD or digitizer.
If your device is still loose, it may be because the 6s has light adhesive between the display assembly and frame, which your replacement may not have. You may be able to substitute 1mm Tesa tape (Tesa 61395 Tape) to help secure the loose portion. I haven't tried this myself, but I have used that tape for similar fixes on other devices to great success.
If your display was broken because of drop damage, it may be that the frame was bent in the impact. This seems to be a particular problem for the 5 and 5s, but it may happen in the 6s as well. There's not much you can really do about that. If this is your problem I'd suggest keeping your phone in a case and regularly praying to whichever deity you prefer that everything holds together.