Maybe he thought if he did it again, he'd get another treat

Maybe the treat you gave him did that

Looks like it's time for new treats.

He's just a pup babies will do that. I've found verbal praise and touch works better than food.

Dogs will learn to go outside when there business. Bet every dog I have had will start to wretch of they have hard wood, concrete, grass or carpet it will always be the carpet.

It wasn't his fault. Sometimes my older dog still gets sick (very rarely, and when it's very bad we understand why she couldn't get outside fast enough). Hope his stomach feels better :)

good boy.

spewed up the treat, or it's business?

I think it's his way of telling you to get better treats.

I find verbal humiliation works best on puppies.