As discussed in this great answer, it is convenient to introduce a local coordinate system on top of the image.
\documentclass{beamer}
\usepackage{tikz}
\begin{document}
% based on https://tex.stackexchange.com/a/9562/121799
\begin{frame}
\frametitle{\only<1>{Draw a coordinate system on top of the image}%
\only<2>{Draw the text nodes (with some generous inner sep)}%
\only<3>{Connec the text nodes to the points}%
\only<4>{Remove the grid}%
}
\begin{tikzpicture}
\node (image) at (current page.center) {\includegraphics[scale=0.5]{tj}};
\begin{scope}[shift={(image.south west)},x={(image.south east)},y={(image.north west)}]
\only<1-3>{
\draw[help lines,xstep=.1,ystep=.1] (0,0) grid (1,1);
\foreach \x in {0,1,...,9} { \node [anchor=north] at (\x/10,0) {0.\x}; }
\foreach \y in {0,1,...,9} { \node [anchor=east] at (0,\y/10) {0.\y}; }
}
\only<2->{
\node[fill=white,font=\large,inner sep=4pt] (Tom) at (0.9,0.74) {Tom};
\node[fill=white,font=\large,inner sep=4pt] (Jerry) at (0.9,0.23) {Jerry};
}
\only<3->{
\draw[ultra thick,red] (Tom) -- (0.49,0.42);
\draw[ultra thick,red] (Jerry) -- (0.66,0.23);
}
\end{scope}
\end{tikzpicture}
\end{frame}
\end{document}

Of course, in the end you may want to erase the grid.
\documentclass{beamer}
\usepackage{tikz}
\begin{document}
% based on https://tex.stackexchange.com/a/9562/121799
\begin{frame}
\begin{tikzpicture}
\node (image) at (current page.center) {\includegraphics[scale=0.5]{tj}};
\begin{scope}[shift={(image.south west)},x={(image.south east)},y={(image.north west)}]
\node[fill=white,font=\large,inner sep=4pt,align=center]
(Tom) at (0.9,0.74) {Bad\\ Tom};
\node[fill=white,font=\large,inner sep=4pt,align=center] (Jerry) at (0.9,0.23)
{Tasty\\ Jerry};
\draw[ultra thick,red,-stealth] (Tom) -- (0.49,0.42);
\draw[ultra thick,red,-stealth] (Jerry) -- (0.66,0.23);
\end{scope}
\end{tikzpicture}
\end{frame}
\end{document}

Note that you were using remember picture,overlay
without actually using it. As long as you do not really make use of it I recommend dropping it. I also added the arrow heads and multiline nodes, as asked in the comments.