The matrix is hermitian yes, but the signal is assumed to exist on a 2D discretized grid representing a function. And hermitian matrix means something different than hermitian function.
With overline meaning complex conjugate. For functions of two variables the hermitean property gives : $$f(x,y) = \overline {f(-x,-y)}$$
For example in the language if you write
fftshift(fftshift(fft2(rand(3)),1),2)
you will get the 2D Fourier transform of a real valued random function uniform on $[0,1]$ sampled in three spots, -x,0,+x and -y,0,+y respectively.
The result is:
$$\left[\begin{array}{ccc}
-0.0273+0.0188i&-0.7306-0.2549i&0.7398+0.2131i\\
-1.4214+0.2657i&4.5929+0i&-1.4214-0.2657i\\
0.7398-0.2131i&-0.7306+0.2549i&-0.0273-0.0188i
\end{array}\right]$$
And you can see for yourself which real and imaginary parts match up and how the sign changes.