1. Taim wasn't initially DF, just somebody who legit believed he was the DR. Rand's trust in him when he appointed him atop the BT was justified, he put an ally up there. He may have been a mean, own agenda guy but still an ally.

2. Taim, like Demandred before him, went to the DO gradually after recieving honours from the Rand/LTT. When LTT gave Demandred honours and positions, LTT was exercising his dominance over Demandred which really bothered the latter. The same seems to have occured with Taim. He likely had a personality that made his transition into a DF and subsequent dreadlord quite smooth (while Logain, another false Dragon, is not somebody who would become a DF as he is happy being in Rand's shadow and finding his own glory in that position) but needed that little extra push to get him there.

It makes the whole situation more interesting for me to think that Taim wasn't forced over to the DO nor was he always a DF. It mirrors the LTT/Demandred relationship nicely. In a way, Taim is Demandred just figuratively and not literally as some have suggested.