OK, testing (but I happen to be in HDRI right now and don't know if this is an issue):
#measure your rgb colors
convert colorsample.jpg -scale 1x1! txt:-
# ImageMagick pixel enumeration: 1,1,255,rgb
0,0: (238,208,200) #EED0C8 rgb(238,208,200)
#create new test swatch as png (to avoid jpg compression color changes)
convert -size 100x100 xc:"rgb(238,208,200)" colorswatch.png
#measure the HSL colors of colorswatch.png
convert colorswatch.png -scale 1x1! -colorspace HSL txt:-
# ImageMagick pixel enumeration: 1,1,65535,hsl
0,0: ( 2299,34588,56283) #08FB871CDBDB
hsl(3.50877%,52.7778%,85.8824%)
#modulate colorswatch
convert colorswatch.png -modulate 100,270,100 colorswatch_mod_100_270_100.png
#measure the HSL colors of modulated image
convert colorswatch_mod_100_270_100.png -scale 1x1! -colorspace HSL txt:-
# ImageMagick pixel enumeration: 1,1,65535,hsl
0,0: ( 2702,65535,54317) #0A8EFFFFD42D
hsl(4.12358%,100%,82.8824%)
So either the hue and lightness are getting changed slightly (hue from 3.5 to 4.1 and lightness from 85.8 to 82.8 ), or it is precision, or it is my HDRI, or hsl color measurement is off some?
By the way, you can only increase the saturation so much, so once it reaches 100% that is all you can do. So you started with 52.8% saturation. Anything more than about 200 in modulation (i.e. 2x) will make it fully saturated or at 100%, which is what you have achieved. The hue and lightness have not changed that much. But indeed they are somewhat different.
NOTE: I did everything in HSL as -modulate uses HSL as default rather than HSB.