Moving tikz node scales coordinates in scope

UPDATE

I don't think grid is the right way to annotate the image. Cauze grid is the high level command of pgfpathgrid with which

Conceptually, the origin is part of the grid and the grid is clipped to the rectangle specified by two points. However, no clipping occurs (this command just adds parts to the current path) and the points where the lines enter and leave the “clipping area” are computed and used to add simple lines to the current path.

I define a new coordinate system img cs to help the work.

documentclass[tikz, border=1cm]{standalone}
usepackage{xparse}
makeatletter
newififxtick@rotate
tikzset{
  img/.cd,
  x/.store in=img@x,
  y/.store in=img@y,
  node/.store in=img@node,
}
tikzdeclarecoordinatesystem{img}
{%
  tikzset{img/.cd,#1}%
  tikz@scan@one@pointpgf@process([email protected] west)
  pgf@xa=pgf@x
  pgf@ya=pgf@y
  tikz@scan@one@pointpgf@process([email protected] east)
  pgfmathparse{(1-(img@x))*pgf@xa+(img@x)*pgf@x}
  pgf@x=pgfmathresult pt
  pgfmathparse{(1-(img@y))*pgf@ya+(img@y)*pgf@y}
  pgf@y=pgfmathresult pt
}%
NewDocumentCommand {picgrid} {O{10} O{10} D(){} O{}} {
  pgfkeys{/pgf/number format/.cd,fixed,fixed zerofill,precision=2}
  foreach i [evaluate=i as x using i/#1] in {0,...,#1}
  draw[#4]
    (img cs:node=#3, x=x, y=0)
    node[rotate=-90, anchor=west] {pgfmathprintnumber{x}}
    -- (img cs:node=#3, x=x, y=1);
  foreach i [evaluate=i as y using i/#2] in {0,...,#2}
  draw[#4]
    (img cs:node=#3, y=y, x=0)
    node[left] {pgfmathprintnumber{y}}
    -- (img cs:node=#3, y=y, x=1);
}
makeatother

begin{document}
begin{tikzpicture}
  node[anchor=south west, inner sep=0] (a)  at  (.5, .6) {includegraphics[width=0.9textwidth]{example-image}};
  picgrid[20][20](a)[red, thick]
  draw[thick, img/node=a] (img cs:x=.1, y=.6) --
    node[sloped, above] {from (.1, .6) to (.85, .95)}
    (img cs:x=.85, y=.95);
end{tikzpicture}
end{document}

old answer

<coord-1> grid <coord-2> means draw grid on the rectangle which is specified by <coord-1> and <coord-2>. Let's see where <coord-1> -- (0, 0) and <coord-2> -- (1, 1) actually lay on your second picture:

As you see, there is nothing wrong.

So what's wrong with your third picture? Let's draw x unit vector and y unit vector of your scope: Ahha, x = -y, which means any coordinate like (i, i) actually is (0, 0). So (0, 0) grid (0, 0) does nothing.

documentclass[tikz, border=1cm]{standalone}
usetikzlibrary{positioning, fit}
usetikzlibrary {arrows.meta}
tikzset{
  direct/.style={
    line width=1pt,
    arrows={-Stealth[length=3mm, width=3mm, #1]}
  }
}

begin{document}
begin{tikzpicture}
  node[anchor=south west, inner sep=0] (image2)  at  (.5, .6) {includegraphics[width=0.9textwidth]{example-image}};

  begin{scope}[x={(image2.south east)},y={(image2.north west)}]
    draw[direct, green] (0, 0) -- (1, 1);
    draw[thick,red, opacity=0.5, xstep=.1,ystep=.1] (0,0)  grid (1,1);
  end{scope}
end{tikzpicture}

begin{tikzpicture}
  node[anchor=center, inner sep=0] (image3)  at  (0,0) {includegraphics[width=0.9textwidth]{example-image}};
  % show x, y vector
  draw[direct, red] (0, 0) -- (image3.south east) node [red, right] {$y$};
  draw[direct, blue] (0, 0) -- (image3.north west) node [blue, left] {$x$};
  begin{scope}[x={(image3.south east)}, y={(image3.north west)}]
    draw[direct, green] (0, 0) -- (1, 1);
    draw[thick,red, opacity=0.5, xstep=.1,ystep=.1] (0,0)  grid (1,1);
  end{scope}
end{tikzpicture}
end{document}