In the 1987 Teenage Mutant Ninja Turtles cartoon, we are told
It was a powerful mutagen. It caused whoever touched it to take on the form of whatever animal they had most recently been in contact with. The turtles started becoming human as they had most recently been with Yoshi.
This explains why the turtles become half-human, as Splinter picks them up to clean them.
But Splinter continues...
But Yoshi had most recently been with... the rats.
Except, Yoshi just handled the turtles. Why didn't he turn into a half-turtle too?