The plot is complex, but if you bear with it, it'll make sense:
Roth chose to kill Michael after Anthony's First Communion party because he knew Frank Pentangeli would be there, contentious over the Rosato Brothers, whom Michael and Roth favored over Frankie. Thus Frankie had the perfect motivation to kill Michael--and would make the perfect fall-guy for the crime. The assassination attempt against Michael failed. But when Michael visited Roth in Miami, Roth was heartened that Michael, as he expected, blameed Frankie for the attempt. He promised to kill Frankie (“Frank Pentangeli is a dead man”), and even asked Roth's permission (“You don’t object?”)! Ah! Roth saw a silver lining in the cloud of the botched assassination: Michael would kill the obstreperous Frankie without his having to lift a finger or spend a dime! Heh-heh! BUT:
Instead of killing Frankie, Michael dispatched him to settle his problems with the Rosato Brothers. Oh-oh! Roth knew Michael would never give a pass to a mortal enemy. Now it was certain that Michael didn't suspect Frankie in the Tahoe attack—leading to the possibility that he did suspect Roth. SO:
Roth ordered the Rosatos to kill Frankie at their meeting. That way, he'd eliminate Michael's chief NY ally before the two of them could cook up any mischief against him. To maintain his façade, Roth could always claim that he’d only done what Michael said he was going to do anyway. (Later, in Havana, Roth implied that Frankie’s assassination was tit-for-tat for Michael’s murder of Moe Green.)
Bear in mind that Roth intended for the Rosatos to kill Frankie in that bar, and for his pal Batista to kill Michael in Havana. But when both failed, Roth improvised brilliantly: he reached for the Senate lawyer Questad (who belonged to him) and arranged for Frankie's survival to be kept secret. That way, Roth (through Questad and the Senate committee) nearly trapped Michael into going away for five years each on five counts of perjury.