You will need to configure Texmaker to work with Better BibTeX. First, command Texmaker to use a function called
biber that interprets the Better BibTex generated cite keys.
From the Texmaker toolbar, navigate to: Options > Configure > Commands.
In the Bib(la)tex window replace the default command (probably 'bibtex %.aux') with 'biber %'. This commands Zotero to use the correct citation formatting when compiling a document. Be sure to remove the quotation marks around the command. Note that the command is all lower case and there is a space between the word and the percent symbol.