The word processor plug-ins apply the “default” (LibreOffice/OpenOffice) or “Normal”/“Standard” (Word) style to generated citations and the paragraph in which they are inserted. The bibliography is rendered in a different style - “bibliography”. As a result, inserting a citation with Zotero can remove formatting (such as indents, line-spacing, font size, etc.) from an entire paragraph and the citation can appear in an unwanted font or format. You can correct the formatting by adjusting the standard/default style (for citations) and the bibliography style (for the bibliography) in your word processor.
If your styles and formatting toolbar is open (it is a pull-down menu with a list of labels such as “Normal”, “Body Text”, “Heading 1”) you can simply right-click on the “Normal” or “Bibliography” style and format it. Otherwise, select “Styles and Formatting” from the Formatting toolbar or the Format Menu. See here for the official Microsoft instructions, and here for a longer guide with screenshots.
In the “Home” Tab, first click on “Font” tab and choose the font and font-type you want to use and select “default” on the bottom of the window. You can change paragraph formatting (such as line spacing, indents, etc.) by doing the same on the “Paragraph” tab. There is also a “Styles” tab, where you can modify the “Normal” and the “Bibliography” style. See here for a guide with screenshots.
In LibreOffice, open the styles manager in “Format” –> “Styles and Formatting” or by hitting F11 (F12 in OpenOffice). Right click on “Default” or “Bibliography”, select “Modify”, and make the desired changes to this style.