The Principate began with traditional republican voting. Augustus had restored such procedures during his reforms. He passed a law in ad5, the Lex Valeria Cornelia, which set up a special advisory body of senators and decurial equites (senior plebs with civic responsibilities) to produce a list of favoured candidates called destinati before the Comitia. There's some debate over this especially because this body appears to have waned in importance by ad14. In any case, Tiberius transferred these elections to the Senate when he came to power.
There is a hint in a document called the Tabula Hebana which suggests that better control of voting was to offset the risk of public riots. Tiberius had a stricter control over voting than Augustus, though this was not the case after Tiberius set up semi-retirement in Capri. By then the Senate had much more freedom to control voting and no doubt the ideas to remove voting from the plebs completely starts from that moment, as the Senate begin to find ways to avoid setting issues for the popular assemblies to vote on. It was easier to seek guidance from the senior man among them, the Princeps Senatus, or Princeps, or if you really have to use the word, Emperor, who might in theory prove an excellent scapegoat. The Senate had never liked sharing their privileges in governmental business with lower classes or outsiders. Tacitus holds that Tiberius influenced the selection of candidates by speeches, not by decisions. None of the Roman writers say that the Princeps controlled the Comitia.
Dio tells us that the people continued to meet for elections. The Princeps appears in general to have intervened to prevent unsuitable candidates, such as those who canvassed or bribed their way into consideration, or perhaps for something as simple as personal dislike, but tended otherwise to let the Comitia vote as per tradition. There were exceptions such as Egnatius Rufus who got himself considered for consulship in 19BC and only the previous Consul managed to impede him.
However, it is noted that Tiberius was only allowing enough candidates to fill the position, not to allow choice and this at a time when Tiberius was said to be refusing extra powers from the Senate, but this might not actually be the case as we know the Senate were asking for extra candidates and so Tiberius was simply acting to mediate the voting for the same reasons Augustus sought to.
There were some public disturbances over voting during the early Principate, Augustus had Agrippa keep order in Rome, and it seems the caution exercised by the Roman leaders was justified. In ad7 a riot was so bad that Augustus chose to appoint magistrates directly.
Although the Princeps made recommendations about candidates, the Senate continued to do business as they had in the late Republic, by filling posts by merit, agreement, or lot.
By the time Caligula comes to power, the period of riots has gone, replaced by considerable apathy which no doubt suited the Senate entirely. The mechanism existed, persisted, but was essentially pointless as too many decisions were being made outside of the Comitia's reach.
So intervention from the Princeps was a matter of expedience rather than the exercise of power, with the Senate taking advantage of change to assert their dominant role in government.