Well, I'm not so sure he did form his own family--literally:
In the fishtank scene, Clemenza says to Vito, formally:
"Don Corleone -- you once said that the day would come when Tessio and me could form our own Family [emphasis added]. Til today, I would never think of it. I must ask your permission..." Vito defers to Michael, who replies, "After we make the move to Nevada -- you can break off from the Corleone Family and go on your own. After we make the move to Nevada."
Note that the transcript uses "Family" as singular, implying that Clemenza and Tessio would jointly form a single family. Didn't sound like a workable arrangement, given the differences in temperament and territories twixt Clemenza and Tessio. Puzo resolved it by having Tessio taken for a ride. But the question remains: Did Clemenza form his own Family? Was he an independent entity?
By GFII, we learn that the Family "is still called Corleone" and Frankie Pentangeli is a caporegime, reporting to Michael. Did the family suddenly revert to "Corleone" and to Michael's control after Clemenza died? I doubt it. I'm guessing that Michael, obsessed with controlling everyone and everything, would never have relinquished total control over the "olive oil business" in New York. I think he made an arrangement with Clemenza--whose loyalty was unquestioned and who was well respected by his men--to nominally report to Michael as a caporegime. But Michael probably gave Clemenza a long leash, and very little actual supervision, because Clemenza needed little supervision. Clemenza probably didn't protest--he was getting old, no doubt in declining health, most likely was satisfied with the arrangement and didn't think it worth fighting over.
Frankie was another story. I'm guessing he was weaker and less respected than Clemenza (attest his having to bring his dispute with the Rosato brothers to Michael). Michael probably kept him on a much shorter leash--and, as we saw, Frankie bridled under it. In fact, I'll guess that there was a power struggle after Clemenza died (perhaps with the Rosatos), and Michael made Frankie an offer he couldn't refuse: I'll support you as chief of the NYC branch, but you have to be under my thumb more than Clemenza was.