It makes me think Demandred and Taim were never directly involved prior to the BT. Clearly Taim had learned many things from Ishamael prior to the events of the series, he already knew how to test men and was obviously a somewhat accomplished Channeler when he arrived in Caemlyn. When the opportunity to become M'Hael presented itself I doubt it is what he expected, but he obviously saw the advantage quickly and IMHO presented the idea to the newly reborn Moridin. It is plausible that Moridin as Nae'Blis or possibly Shadar Haran ordered Demandred to teach Taim about the infrastructure for a military organization etc ... We see Semirhage being used in a similar way to give Aran'gar a solid backstory so it doesn't seem far fetched to me.

What you outline above could be accurate, but I tend to believe Taim has always been Ishamael/Moridin's creature. I can't imagine Demandred relinquishing control of such a powerful tool as the Asha'man and Taim.