There are certain features with some requirements for the mesh, like root motion. You would need to have a ground anchored root bone in your model’s skeletal mesh in order for that to work. (Warping is also used in motion matching which needs root motion to be enabled so that’d mean it’s also a requirement in this case) But motion matching as it is doesn’t really have a standard animation type like you suspect, at least nothing particular comes to my mind currently.
Now, about your issue! The animations in Unreal’s sample project which you’re probably using have hundreds of variations to fit in any given situation, so the lack of animations could be why you get that feeling. Also, if you’re using a custom model and retargeted the sample animations to it, maybe there could be imperfections there as well. You can test that by playing standard animations with no extra thing going on in the background and compare the models side by side. If you notice something’s off, you can try manually setting up the retargeter which you probably auto-generated.