no, the line you cite concerns disambiguation if two different authors have the same last name.
I'd generally recommend that you have a look at a couple of styles that look similar to what you need using the chrome pane:
chrome://zotero/content/tools/csledit.xul

Also, with problems about citation styles it would help to post your csl code.

Specifically, you seem to want something like this:
somewhere in the beginning define something along the lines of:

<macro name="author-short">
<names variable="author">
<name form="short" and="text" delimiter=", " initialize-with=". "/>
<substitute>
<names variable="editor"/>
<names variable="translator"/>
<text variable="title"/>
</substitute>
</names>
</macro>

and then in the beginning of the part that's labeled citation,
change what is probably
<text macro="author"/>
to
<text macro="author-short"/>

sorry, I don't understand.
please be more explicit about what exactly you want and what you have tried.
So first, please give some specific examples of citations and how you want them to look.

Then, please post your csl code or tell us from which code you have been working and what exactly you have tried.

The Journal of Neuroscience looks good to me at first glance. the chrome pane displays in text citation as (McCarthy, 1996) - is that not what you want?

on the chrome pane - is that the case for all author date styles? (check, for example, Harvard Reference Format, Chicago Style (Author Date), APSA and ASA.
When you cite using the word plugin or drag holding the shift key - same result?

Thanks for the indications.