"Tease sb. sth." doesn't work. Actually, "tease" really has nothing to do with what you're seeing here.
What you're seeing in your quote is a very specific, informal sense of "something" where "something" is an adverb which must be followed by an adjective. It is mostly used with only a handful of (essentially synonymous in this context) adjectives: terrible, awful, fierce, good.
As you said, the expression "something adj" essentially treats the adjective as an adverb. You can't however, just substitute in the adverb directly in all cases. For example, it may need to be moved:
I’m hungry something terrible. [= "I'm terribly hungry."]
Amanda, Bibliomaniac (blog), Mar. 21,
The reason why "something adj" is used instead of the adverb is because it adds emphasis. In this context, it might also be used because it sounds a little dated (Myrtle is old, after all.)
Also, there's a superficially similar form that doesn't have the same meaning:
I shook something fast. [= I shook something quickly.]
Compare with "I begun to shake something terrible". There's no magic formula to decide which meaning is intended, so you have to decide which meaning makes the most sense pragmatically. (It's also relevant to note that according to my Google searches, "something" is rarely used as an adverb.)
See also the examples numbered 18 in this tangentially related PDF.