I'm having this issue with this rig I worked on.
If you notice, the legs and arms are delayed from the rest of the body in the viewport. I thought it would be ok once I exported this as fbx, but apparently this lag gets baked into my exports and I end up having to import my fbx file, and cleaning up the raw Deform joints to make the animation passable.
This rig has an IK/FK slider along with the ability to match FK controls to the IK controls and vice versa. So I figured all of that would be an issue, so I've tried a version where I delete all the set driven keys, but it still lags.
I read on a few posts that suggest a rebuild of the IK constraint fixes it. So I did that too, but once I close Blender and open the file up again, the issue comes back.
I've tried opening this file in Windows 7, Linux Mint and Fedora 26 and the issues is still there. My specs are: AMD FX-8320 16GiB RAM NVIDIA GeForce GTX 950