The Concordance function will only search the Background Read-Only TM if no hits are found in the active TM.
If the option Search First in Background TM is checked, Concordance will first search the Background Read-Only TM, and only if no hits are found, it will proceed with the active TM.
What if you want hits from both active and background TM? There appears to be no provision for this; but there is a workaround.
Export your active TM and add it to your Background Read-Only TM. Thus, you will have matches from both.