I’m not talking about the mannequin to the right in Blender really, I’m talking about the skeleton in UE4 which you will retarget the animations from. I’m not talking about axes (bone roll) either, I’m talking about bone orientation in the 3d space. If they are different you will get a result like in the picture you posted. For example the arm bones in your rig are straight, in the UE4 skeleton they are slightly bent in the front view, and also the top view.
As I said earlier you can change the retarget base pose when retargeting by rotating the bones in Persona, clicking the button in the retargeting manager( View Pose or whatever it was called) then clicking Use Current Pose. Doing this takes a long time and you’re not guaranteed to get a perfect result. That’s why I recommend using the UE4tools rig which matches the UE4 mannequin skeleton perfectly without you having to change anything (except renaming the rig in Blender to “armature” to remove the armature as an extra bone).
I’m using UE4tools in the latest Blender version and it works perfectly.