As of the latest release (1.14.3), tamed animals (wolves, cats, parrots) teleport to the player as it should when the player is a little ahead. (Except in the snow... see MC-145021)
However, this doesn't seem to work propely in the latest snapshot/pre-release(s) of 1.14.4.

Things they don't proper teleport in this pre-release:
1: When they are in water and the player is on land, animals don't teleport to the player instantly. They will instead teleport when they hit a block on the surface.
2: Even walking/running on normal lands, they don't propely teleport until they jump or fall down 1 block when the player is a little ahead.

(Screenshots are below for reproducion)