According to the phrase finder, it is a variation of ass end over teakettle and actually ngran shows that its usage started a few years later He got the business end of a sword 'tail is probably used with reference to previous versions which used 'ass or butt.' to me it's most likely just one of those made up sayings.
TUSHY on Twitter: "She does a thing called what she wants and we're here for it 💖
The connection between the baby and the spank on the tushy is pretty well engrained in the american psyche, i believe
By the way, another americanism is as cute as a baby's bottom, (or sometimes smooth as a baby's bottom) which adds another wrinkle to the notion of brand spanking newness.
He is getting the brunt of the joke He is getting the raw end of the deal