If you will notice, Joe Jackson's name is followed by five different tags and he has only one album tagged Jump Blues, and that album is "Jumpin Jive". That album was tagged as Jump Blues because its a straight up jump blues album without the sort of self-aware ironic kitsch that goes into a modern day exotica album.

Joe Jackson's album is fairly sincere and far different from the more nuanced and complicated approach of the Squirrel Nut Zippers' albums.

Likewise, Roomful of Blues puts out more or less straight up jump blues albums with little sense of the sort of irony and kitsch that is usually associated with exotica.

Tagging Squirrel Nut Zipper albums is not easy, some more lazy music sites tag them as jump blues because their albums can contain jump blues songs, but their albums also contain a myriad of other styles as well. 

All the same, we have to put some tag on the albums or they can't be added. The Zippers are a San Francisco band, and like other SF bands of their ilk, the Zippers pay a lot of attention to the total package, particularly appearance and nuance. You can bet much period knowledge goes into their presentation and this is what led to exotica being their best tag. They are a blend of many styles and anachronistic settings, all done with a degree of self aware ironic hipness, very much a San Francisco band. Joe Jackson could never understand all this and he doesn't need to.

The so called "swing revival" fad of the mid to late 90s was not so much about real swing music, but often had more to do with jump blues, or even rockabilly. The Zippers were one of the bands that helped kick off that fad, but their music was different from their imitators.

The Zippers were actually knowledgeable about a lot of early jazz (20s etc) as well as other early American music. The music they played was often very sophisticated and authentic and covered a lot of pre-swing music. 

Much of the bands that followed in the so-called 'swing revival' were not so near talented or knowledgeable as the Zippers. As always, I was a working musician at this time and watched in disgust as so many musicians jumped on this phony 'swing' bandwagon. Much of the music was just the same old corny blues and rockabilly, just dressed up in different drag.

Our Swing section at JMA is for real swing music, the Zippers are too diverse to be a swing band, although they do play their share of swing music and play it very well.

especially: literary or artistic items having an exotic theme or nature
As to the music,some unusual way to perform I think, like playing jass on a piano