Then when did Pentangeli enter the picture? When Michael visited him in NY, he said he was "very glad this house didn't go to strangers--first to Clemenza, then to you," implying a direct succession.

With Rocco in Nevada (instead of NYC, per the novel), Cicci provides NYC continuity between GF and II. As we know, FFC wanted Castellano to reprise Clemenza in II, but they couldn't come to terms. Hence Pentangeli, and Cicci as his subordinate.