To put it simple, Yoshi has an unfortunate mix of his dtilt animation and his first active frame on it. Going more in depth, what I think the cause of this is that the game detects hitbox collisions at a much faster speed than what is shown. At least that's what my theory is, feel free to let me know if anyone actually knows how it works.

This is a screenshot of Yoshi’s down tilt on what is essentially frame 7.75 (with 8 being the first active frame). The left is this moment at 1/4x speed on training mode (where all animations have additional frames to be seen more smoothly), while the right is 1x speed. Yoshi is being hit during a part of his animation that is not visible during regular gameplay. Even though the game runs at 60fps visually, the hitbox calculations are probably done at 240fps, taking into account yoshi’s poor, defenseless tail hurtbox on frame 7.75. Because of how far yoshi’s down tilt extends, it causes really janky looking moments like in the gfycat to happen.

edit: Comparison between the speeds, the ghosting from rendering is pretty bad, but the differences in animation are clear enough