That's very strange, because as I said, it should change the emoji to the selected skin tone immediately and leave it at that unless you select a different one.
It even keeps multiple skin tone options available in the "Frequently used" section of the keyboard for the same emoji. Make sure you are tapping not on the yellow one there if its still there, but the more recently used versions. Eventually the other color should fall off the recently used.
In the image below I have 3 different skin toned women and 2 different face palms and 3 different shrugs.
The Emoji itself in the regular location, stays at the last skin tone that was used.