@cyclonenic sorry about putting you wrong in my above post.
So here's how it works. Let's use a dog playing in puddles as the example.
My sim has caught his dog playing in puddles at least 5 times. Each time he lectured his dog about not doing this action. The dog stopped each time but nothing else really happened.
On the approx 6th time my sim lectured the dog again about not playing in puddles and finally the notification came that "'dogs name' has learned to not play in puddles" and a musical tone/sting played to alert me the player that something had happened.
Now it seems that the aspiration must be chosen at the time. Only when the Friends of the Animals aspiration was the active one did the counter acknowledge that the pet had 'successfully been trained out of a misbehavior'.
This was what threw me as I expected it to count even if my sim had another aspiration chosen at the time of doing the lecturing.