Any process that increases the activity of a transcription factor that activates transcription of Hedgehog-target genes in response to Smoothened signaling. In Drosophila, Cubitus interruptus (Ci) is the only identified transcription factor so far in the Hedgehog signaling pathway. In vertebrates, members of the Gli protein family are activated in this way. Activation of the Gli/Ci transcription factor is distinct from its stabilization, when proteolytic cleavage is inhibited.