How to prevent \cite at the end of the sentence start a new line with a dot

The code you pasted in pastebin defines the guts of \cite as follows:

\def\@cite#1#2{{$^{\mbox{\scriptsize $#1$}}$%
    \if@tempswa , #2\fi}$^{\mbox{\scriptsize $)$}}$ }

The last space, immediately before the final closing brace, has got to be a mistake. It separates the punctuation that follows, with the result that LaTeX can break the line there.

To fix the problem, do not edit the style in place. If you do, and submit your LaTeX source to the journal, they'll use the buggy style and your work will be for nought. (But do tell the creators of the style about the bug). What you should do is put the fixed version in the preamble of your document, after \usepackage{evocomp}, like this:

\makeatletter
\def\@cite#1#2{{$^{\mbox{\scriptsize $#1$}}$%
    \if@tempswa , #2\fi}$^{\mbox{\scriptsize $)$}}$}
\makeatother

Do this and you won't need to mess with \hboxing your citations anymore-- they'll work as they're meant to.