There was a similar question about a month ago, answered by u/Alkibiades415 (who could probably answer this one as well, better than I can!), about Mark Antony’s speech at Caesar's funeral.

Lucky for us, the sources for the funeral speech and the assassination are the same, and they also tell us that yes, the public knew right away that Caesar had been murdered by senators. The assassination took place inside the senate chambers, out of sight, but the information was spread immediately by people who were outside or nearby when it happened.

Caesar was accompanied by a crowd of admirers as he went to the Theatre of Pompey, where the Senate meeting was being held, so there were still lots of people outside. It was also just a regular day for everyone else, so there were lots of people in the Forum. People were also watching a gladiatorial spectacle elsewhere in the Theatre.

According to Appian:

“…there was an immediate flight throughout the curia and throughout the whole city. Some senators were wounded in the tumult and others killed. Many other citizens and strangers were murdered also, not designedly, but as such things happen in public commotions, by the mistakes of those into whose hands they fell. Gladiators, who had been armed early in the morning for that day's spectacles, ran out of the theatre to the screens of the senate-house. The theatre itself was emptied in haste and panic terror, and the markets were plundered. All citizens closed their doors and prepared for defence on their roofs.”

According to Nicolaus of Damascus:

“A tremendous uproar arose from those who had no knowledge of the plot and who were rushing terror-stricken from the senate house, thinking that the same awful thing was going to happen to themselves also; and from those of Caesar’s associates who were outside and who thought that the whole senate was involved and that a large army was on hand for the purpose; and from those who, ignorant of the affair, were terrified and thrown into confusion from the suddenness of the noise and from what burst upon their view - for all at once the assassins [rushed out], with bloody daggers in their hands. The whole place was full of people running and shouting. There was a crowd, too, in the theatre, which got up and rushed out in disorder (there happened to be a gladiatorial exhibition in progress) knowing nothing definite of what had happened but frightened by the shouting all about them. Some said that the Senate was being slaughtered by gladiators, others that Caesar had been murdered and that his army had started to pillage the city; some got one impression, others another…There was much running in the streets and through the forum, now that the news that Caesar had been murdered became known to the throng.”

Caesar’s crowd of admirers all fled, but Appian says three slaves eventually came back and brought his body to his wife. The assassins tried to convince the city that they had killed a tyrant and restored their freedom, but the people were not as happy about this as they expected. Things got so chaotic that Lepidus even brought a legion into the city.

Unfortunately these aren’t exactly eyewitness accounts…Nicolaus was a contemporary but he didn’t live in Rome. Appian and Suetonius were Romans but were writing about 200 years later, so they weren’t eyewitnesses either (Suetonius’ account is here but he doesn’t mention how the city reacted). But it seems pretty clear that everyone who was outside the Theatre of Pompey and perhaps in the rest of the Forum knew immediately, because the senators rushed out with their bloody daggers and told everyone. The rest of the city found out soon after although rumours spread faster than the truth.