The MWE example presented contains some conceptual errors.

The most relevant one, I think, is that you wish to reference nodes through their text and not through their name. That's what I read in:

\node(a)  [draw,rectangle,text=teal] at (0,0) {here};
\node(b)  [draw,rectangle,text=olive] at (3,0) {there};
\path[measuring south=from here to there is far,fill=red];


The \path syntax should contain a and b, not here and there.

Second, here the late options are used in the wrong manner: once the path is ended, that's it, you can't append stuff anymore. So, in measuring south you are willing to insert path rather than append after command. Moreover, since you are changing path options from the main path to the inserted ones, you may want to use \pgfextra.

This would have been my way to go:

\documentclass[border=3pt]{standalone}
\usepackage{tikz}

\tikzset{dimen/.style={&lt;-&gt;,&gt;=latex,thin,
  every rectangle node/.style={fill=white,midway}
}}

\tikzset{measuring south/.style args={from #1 to #2 is #3}{
        insert path={
          \pgfextra{
                \draw[red] (#1.south west) -- ++(0,-1.0)
                coordinate (A1) -- ++(0,-10pt);
                \draw[blue](#2.south east) -- ++(0,-1.0) 
                coordinate (A2) -- ++(0,-10pt);
                \draw[dimen] (A1) -- (A2) node[midway,fill=white] {#3};
          }      
        }
    }
}

\begin{document}
\begin{tikzpicture}
    \node(a)  [draw,rectangle,text=teal] at (0,0) {here};
    \node(b)  [draw,rectangle,text=olive] at (3,0) {there};
    \path[measuring south=from a to b is far];

  \node(x) [draw,rectangle,text=blue] at (0,-2) {Heaven};
  \node(y) [draw,rectangle,text=red] at (3,-2) {Hell};
  \draw (x.south west) -- ++(0,-1.0) 
            coordinate (A1) -- ++(0,-10pt)
            (y.south east) -- ++(0,-1.0) coordinate (A2) -- ++(0,-10pt)
            [dimen] (A1) -- (A2) node {sin};
\end{tikzpicture}
\end{document}


The result:



Correct use of arguments pattern in pgfkeys/append after command in tikz?
One advantage of a "pre-empt" is quite clear: You take two levels of bidding away from your opponents with a "three" bid. But could that be cutting off your nose to spite your face?

Recently, I had something like KQxxxxx, and a side queen (I forget how the other suits were distributed but was told it didn't matter). My partner was disappointed I didn't "preempt" (in "third" seat). My response was "with seven points?"

My understanding is that people often bid three of a suit with seven cards and this little. Sometimes even less, particularly when non-vulnerable vs. vulnerable. In its extreme version, the mantra is "with any seven (suited) cards."

Isn't this risky? What if we're doubled and only make three or four tricks?
