Monitor calibration and color managed workflow question

Hi,

I bought a Colorvision Spyder and calibrated my monitor.
It really helped. However, I am not really sure how this
works and I fear I might be double-color-managing.

The Spyder generates an ICC profile, puts it somewhere
into windows directory and registers it with the graphics
card. On startup the ProfileChooser takes the default profile
and loads it into graphics card. That means that I am able
to see accurate colors with applications that are not
color managed - web browser, ...

What I do not understand is what happens when I edit the
photo in Photoshop Elements (I do not have the 'big' PS,
so I am not sure whether this is different there). If it
also uses the default profile taken from windows,
I get double color-managing. And I think this is really
the case - when I open the same image in the PSE and
in the default browser, it looks that the result is not
the same - there are subtle differences in skin tones.

How is this supposed to work? Is there any way to have
both the non-managed and managed applications to display
the same (i.e. let the Profile Chooser load the lookup
tables and tell the Photoshop etc. to use sRGB or whatever
the display expects when the conversion is done down
in the LUT)? Or does the PSE _always_ use the default
monitor profile, whatever that is?

Thanks
--
Stano