Just to add to dt's and Olivan'ts excellent posts:
The Fifth Amendment to the US Constitution (part of our Bill of Rights) prohibits defendants from being compelled to testify against themselves. If you are a defendant in a criminal trial, you do not even have to be sworn in as a witness--you can remain silent throughout the trial and let your lawyers do the talking. Most criminal defendants do just that. Juries don't hold it against them--they've seen all those cops-and-lawyers movies and TV shows, and know how a lawyer can tear a witness to pieces. Only very confident--or very foolish--defendants agree to be sworn in and testify.
A Committee of the US Congress (like the one that Michael faced) is not a law enforcement agency, a prosecutor, or a court of law. It can hold investigations and hearings, and has the power to subpoena witnesses. Unlike in a criminal trial, the witness must be sworn in and take the stand. The only Fifth Amendment privilege the witness enjoys is that he can say, "I refuse to answer that question on the grounds that my answer might tend to incriminate me." Gangsters are routinely called before Congressional hearings, and that't the answer they give. If a witness refuses to appear, he can be cited for contempt of Congress. If he lies under oath, he can be cited for perjury. Both will result in serious jail time.
Frankie signed his affidavits against Michael as part of his deal with the authorities: he'd implicate Michael, and they'd protect and take care of him for the rest of his life. But signing affidavits didn't mean that Frankie had to testify against Michael--it was, as far as he and the FBI knew, simply "insurance" in case they had to use the affidavits against Michael. I'm sure the FBI was reasonably certain that Michael would "take the Fifth" when asked those embarrassing questions. That's what all previous gangsters did when called as witnesses. As far as they were concerned, it'd be tantamount to admitting guilt. If Michael were asked "Were you responsible for the murders of the heads of the Five Families in 1950," and he replied, "I refuse to answer that question on the grounds that my answer might tend to incriminate me," what would that tell millions of viewers watching the hearing on TV--that he was, in fact, responsible for those murders. Although Michael couldn't be prosecuted for perjury with that answer, his "legitimate" front would be destroyed. And there'd be no reason for Frankie to testify, or for his affidavits to be used. He would, as he probably assumed, disappear from sight.

But Roth knew that Michael (unlike other major gangsters), was obsessed with appearing legitimate. Through Questadt, he manipulated the Senate committee to catch Michael in a perjury trap by keeping Frankie's survival secret, and tricking Michael into thinking that Cici was the only witness against him. When Cici said he never got a direct order from Michael, he felt he could get away with giving lying answers under oath to those embarrassing questions. Then they sprang Frankie on him. Michael wasn't expecting Frankie--and Frankie wasn't expecting that he'd be needed to testify because he, like the FBI guys, thought Michael would plead the Fifth.