This is a known issue, I think, as it happens with every mount -- there's this tiny little gap between the character and the top of the mount you're on, because they're using the same pose/animations for all mounts as they do chocobos and some of the mounts aren't exactly the right shape/height, and so it's off by a small margin.
From what I can tell, mounts that have unique poses/animations (Crawler, Tiger, Magic Pot) don't have this problem that I can see, because the sitting/standing/whatever animations are custom-tailored to that mount and line up better.
The only advice I can offer the OP is to either always use a Magic Pot until you get Tiger/Crawler, or just ride around in first-person view where you won't notice it.
EDIT: Due to how Fenrir is shaped, the tiny little gap is much less noticeable on him, and Fenrir is always available, provided you do the quest to get him (simply do the same quest you would to get his summon, and choose the mount option when you turn the quest in to get your reward).
Edited, Dec 24th 2016 10:27am by Lyrailis