I enjoyed it but - Is that being fussy? Every time it said it, I thought she was being tsundere, not fussy - and they don't mean the same thing.
They're not the same thing, but they aren't mutually exclusive--"fussy" is a description of behavior, "tsundere" is a specific two-sided character type.
Karin is "fussy" in the sense of being "hard to please or satisfy" (with the further connotation that she loses her temper easily); she's "tsundere" because her fussiness is a mask for her affection.
And Anzu has a Professional Class AAA Tsundere Operator's Certificate.