Perhaps the color profile that Capture One embeds is slightly different than what PS is expecting as sRGB? If this only happens with C1 processed files, I'd shoot an email over to their tech support and see if this is a known issue.
Not all cameras embed a color profile into its JPEGs. Is this missing profile a recent thing or has it always complained? Did you just recently turn on color management? Did you recently check the "ask when opening" files with missing profiles option in your color settings?