I don't think that the part of the instructions you cite means that you have to generate a PDF with hyperlinked references. However, it's possible that they say this somewhere else. Looking back at my last article published with Springer, I notice that I did in fact include a package to enable hyperlinks of this kind to be made. And I don't think that I would have gone to that trouble if I had not had to. So check and see.
Note that (again, unless they have changed their practice since I published with them) you don't actually generate a PDF yourself. You submit a .tex file and any subsidiary files you need (e.g. a .bib file) to their website and the website generates a PDF.
As for inserting each reference manually, no, I'm pretty sure it does not mean that. See egreg's comment. And, as I said, I used BiBTeX when I published with them.
In case it's helpful, here is the (slightly edited) skeleton of the .tex file from my last Springer publication. The hyperref package is the one that creates hyperlinked citations. You will need to submit a .bib file: mine, as you see at the end, was minibib.bib. And you will need to choose a Bibliography Style (to put where I have apalike). Hopefully the journal instructions will have some advice about that. Otherwise just find one that produces something that looks like the bibliographical style for your journal and see if anyone objects. No-one did with me.
\documentclass[nospthms,natbib,final]{svjour3}
%-------------------------------------------------
\usepackage{color}
\definecolor{ink}{rgb}{0,.2,.4}
\usepackage[colorlinks,linkcolor=ink,citecolor=ink]{hyperref}
%-------------------------------------------------
\journalname{Journal of Deep Pofundity}
%-------------------------------------------------
\begin{document}
%-------------------------------------------------
\title{On the Nature of the World}
\author{ng0323}
\institute{ng0323 \at Department of Profundity, Hahvahd U
\email{ng0323@hahvahd.edu}}
%-------------------------------------------------
\date{Received: date / Accepted: date}
%-------------------------------------------------
\maketitle
\section{Introduction}\label{intro}
This article will argue against the pettifogging work of
\citep{influentialguy2013}.
% Insert profound article here.
\begin{abstract}
\keywords{}
\end{abstract}
\begin{acknowledgement}
I am grateful to various people.
\end{acknowledgement}
%---------------------------------------------------------------------
\bibliographystyle{apalike}
\bibliography{minibib}
%---------------------------------------------------------------------
\end{document}
.bblfile that contains the required\bibitemcommands and is read in when the\bibliographycommand is executed. – egreg Jul 14 '14 at 10:30Figure 4 in Section 13 illustrates the results of [42].; encouraging insteadFigure~\ref{fig:SmithResults} in Section~\ref{sec:PriorArt} illustrates the results of \cite{Smith1995}.As already stated by @egreg, BibTeX will be fine. – Paul Gessler Jul 14 '14 at 18:22