There's a great deal of misinformation that keeps appearing and disappearing on this thread.

Yes, the Romans were aware of the Triumvirate, and of the agreement between Pompey, Caesar, and Crassus popularly called the "first" Triumvirate. In reality, there was only one Triumvirate, that of Octavian, Lepidus, and Antony. This was a legally-defined collegiate magistracy, which though extraordinary nevertheless had a legally defined tenure of office, which was renewed several times between its creation and its eventual expiration prior to Actium. There was nothing to hide as far as the Triumvirate went, as it was a public office.

Caesar, Pompey, and Crassus were known to be working together pretty much from the moment it happened. They did not make any great attempt to conceal their cooperation, and openly extended hands to others as well. In a letter to Atticus (Att. 2.3) Cicero mentions that towards the end of December 60, between Caesar's election to the consulship of 59 and his assumption of the office, Caesar sent Balbus to him to offer him a partnership among the dynasts, specifically saying that he would value Cicero's advice as equal to Pompey's, and that he would reconcile Pompey and Crassus. Cicero has some difficulty turning down the offer, since he was following 63 very closely tied to Pompey and, as he says, hoped to resolve the quarrels with his senatorial enemies that had been hovering over him since his consulship, but ultimately he tells Atticus that he can't do it. In April of 59, early into Caesar's consulship and before Cicero started speaking out against him towards the end of the year, Cicero says to Atticus that he doesn't envy Crassus at all for his alignment with Caesar (things were not going well for the dynasts in mid-spring), and apparently Cicero was the original choice for the third dynast.

The dynasts also appeared publicly. If there were any who still weren't aware of their alignment to each other, when the agrarian bill to settle Capua was promulgated relatively early in 59 there could be no doubt. Not only was it strongly in all three men's interest, but in a contio prior to the bill's promulgation Caesar invited Pompey and Crassus to the rostra in order to say whether they supported the measure or not. They did, and apparently made some sort of threatening overture: App. B.C. 2.10 seems to suggest that they encouraged the people to show up to the vote carrying daggers, and Plut. Caes. 14.3-4 says that Pompey threatened to use military force to get the bill, which would settle his soldiers, passed. Bibulus was also invited to a contio, and foolishly accepted--Morstein-Marx has shown that though invitations to contiones were frequently extended to rivals, they were almost never accepted, because as is the case with Bibulus a rival speaking at a contio typically was a target for the crowd's ire, not a legitimate speaker. Yet another indication would have been Pompey's marriage of Caesar's daughter. In May 59, only one month after poking fun at Crassus for siding with the dynasts Cicero has this to say (Att. 2.9):

etenim si fuit invidiosa senatus potentia, cum ea non ad populum sed ad tris homines immoderatos redacta sit, quid iam censes fore? proinde isti licet faciant quos volent consules, tribunos pl., denique etiam Vatini strumam sacerdoti dibaphoi vestiant...

Now indeed, if the power of the senate was so hateful, what then do you think ought to be when it has passed over not to the people but to three unrestrained men? So let them make whomever they wish consuls and tribunes, and let them even dress up Vatinius' tumor with a priest's twice-dyed purple

This is the first surviving written reference to a "rule of three," though App. B.C. 2.9 tells us that Varro published a book or pamphlet called the Tricaranus, or "three-headed monster."

By 56, however, the dynasts' relationship was weakening, since they had gotten what they had wanted and no longer had much need for each other (therefore Suetonius refers to the triumvirate as a "societas," which is not quite a coitio, though Caesar was accused of forming one with L. Lucceius, which was staved off according to Suetonius by Cato's rampant bribery). However, with Cicero returned from exile and Pompey's power over the senate in Caesar's absence significantly weakened, the dynasts reopened their relations at the so-called Conference at Luca in 56. The "renewal" of the triumvirate, if an unofficial agreement can really have official renewal, was a public event. The dynasts got together at Luca in Cisalpine Gaul, and agreed that Caesar should continue prosecuting the war in Gaul and that Crassus and Pompey should share the consulship of 55. With the dynasts at Luca were so many magistrates, promagistrates, and senators that according to Plut. Caes. 21.5 there were 120 lictors at the conference and over 200 senators. App. B.C. 2.17 repeats these figures. An earlier meeting between Crassus and Caesar had already taken place at Ravenna, says Cic. Fam. 1.9. In the same letter Cicero tells us that he himself was in negotiation with the dynasts through Pompey and his brother. Cicero had attempted to drive a wedge between Caesar and Pompey while ostensibly trying to restore the regular function of the state (or more concretely, as Tatum very persuasively argues, trying to get the dynasts to agree formally that Clodius' tribunate was invalid) by reopening the question, settled two years earlier, of what to do about the commission to settle the ager Campanus. When Pompey visited Caesar at Luca Caesar did not like what Cicero had had to say, so Pompey spoke to Cicero's brother Quintus, one of Caesar's legates in Gaul. Cicero says that Quintus reported that Pompey told him:

nisi cum Marco fratre diligenter egeris, dependendum tibi est, quod mihi pro illo spopondisti

Unless you urge your brother Marcus on carefully (i.e. make him shut up), what you promised me on his behalf you'll have to pay.

Quintus had, while heading out to Gaul, tacitly guaranteed his brother's cooperation.