Have you checked the output file directly? I am on Linux Debian. I do this:
exiftool -icc_profile:* <filename.ext>
Example output for 16-bit TIF:
$ exiftool -icc_profile:* 0Y8A7359_01_g.tif
Profile CMM Type : Little CMS
Profile Version : 4.3.0
Profile Class : Display Device Profile
Color Space Data : RGB
Profile Connection Space : XYZ
Profile Date Time : 2018:11:13 11:18:01
Profile File Signature : acsp
Primary Platform : Apple Computer Inc.
CMM Flags : Not Embedded, Independent
Device Manufacturer :
Device Model :
Device Attributes : Reflective, Glossy, Positive, Color
Rendering Intent : Perceptual
Connection Space Illuminant : 0.9642 1 0.82491
Profile Creator : Little CMS
Profile ID : 0
Profile Description : RTv4_Large
Profile Copyright : Copyright RawTherapee 2018, CC0
Media White Point : 0.9642 1 0.82491
Chromatic Adaptation : 0.99995 -3e-05 -3e-05 -5e-05 1.00005 -2e-05 -2e-05 2e-05 0.99974
Red Matrix Column : 0.79771 0.28806 0
Blue Matrix Column : 0.03133 8e-05 0.82489
Green Matrix Column : 0.13516 0.71187 2e-05
Red Tone Reproduction Curve : (Binary data 40 bytes, use -b option to extract)
Green Tone Reproduction Curve : (Binary data 40 bytes, use -b option to extract)
Blue Tone Reproduction Curve : (Binary data 40 bytes, use -b option to extract)
Chromaticity Channels : 3
Chromaticity Colorant : Unknown (0)
Chromaticity Channel 1 : 0.7347 0.2653
Chromaticity Channel 2 : 0.15961 0.84039
Chromaticity Channel 3 : 0.03661 0.00011
Device Mfg Desc : RawTherapee
In my case: Profile Description : RTv4_Large
(I use Adobe ProPhoto output color profile RTv4_Large. but that is just this particular file).
I also use Darktable, but RawTherpaee Wiki has a page where different methods to examine embedded color profile in a picture file output: How to extract and examine ICC profiles - RawPedia
EDIT: Darkroom → Output color profile → export profile is just a default setting for file export for the Output color profile module. It does not state which embedded color profile a tif or jpg file has.
EDIT: Darkroom → Export → profile → image settings means that the profile set in Darkroom → Output color profile will be used, but this can be overridden.