Zap Mama is known for their creative mix of African and European influences, and while they have no direct connection to New Orleans (as far as I know) they were likely drawn to this song because of its similar mix. Interestingly enough, there are no universally accepted meanings to the original lyrics. They were reproduced phonetically by the original lyricists from traditional Mardi Gras chants, so even they are not sure what the lyrics mean! (Ironically, there have been several lawsuits over the authorship of these very lyrics.) Perhaps that gave Zap Mama poetic license to create their own inscrutable lyrics.
Nevertheless I can tell you the following:
"Erurunti sacamona!" is the title of an avant garde poem by poet Dave Brinks, which itself includes a reference to the original "Iko Iko." According to Brinks, the phrase itself is authentic to New Orleans.
Brinks explains the title of the poem as a Mardi Gras phrase, a blend of “Yoruban, Haitian, French and Tchoupic origins,” indicating appreciation for a woman.
"Azucar mama" literally translates as "sugar mama," which is a wealthy woman who keeps younger lovers (like a "sugar daddy") but is probably a reference to the Afro-Cuban salsa queen Celia Cruz, who made "Azucar!" her well-known catchphrase. Celia was another blend of African and European influences.
The reference to "fire" in the lyric is possibly a callback to "set your flag on fire" from the original lyrics, which described one of the tricks the rival groups of Mardi Gras "Indians" would play on each other prior to the great parade --stealing and burning the flag of a rival group.
"Come a come a ne sa le a le": This phonetically reproduced line could have any number of possible meanings depending of if it is French, Spanish or another language, but it could also just be a nonsense callback to the original "Jockomo fin na ne" of the original.
The song originally appeared on the 1999 Zap Mama album A Ma Zone (a pun on "amazon" and "to my place") before becoming much better known on the 2000 soundtrack for Mission Impossible 2. It's not clear if it had already been recorded for the album before being tapped for the soundtrack or not.