How did the senate/military/citizens react to the formation of both triumvirates?
Firstly the First Triumvirate was a private agreement between Julius Caesar (henceforth Caesar) Pompey and Crassus made in 59 BC, it was essentially an agreement to not compete with each other for power, but instead to help each other get what they want. This was a success for all involved the first time so they renewed it with new goals in 56 BC.
The Second Triumvirate in 43 BC was far more than a private agreement between three ambitious men working within a system, it had become far more than that. The actions of Caesar (now deceased) had meant that Octavian, Anthony and Lepidus could go beyond what their predecessors did, and make the Triumvirate official in Roman law.
So the public reaction to the first agreement would be non-existent, as they had no idea it existed. If you want to get an idea of what the Senators thought of it I would suggest reading Cicero’s letters around the time, although the senate only became aware of it when the Triumvirs united to get an agrarian law forced through for Caesar. The senate as you can imagine, did not like these three powerful men working together.
The public would have known about the second triumvirate. But this is where a new problem arises. Our surviving sources for this period have issues. We have the Res Gestae (which is Augustus’ list of accomplishments, understandably biased in his favour), Cicero’s letters (although he was soon killed by the second Triumvirate) Suetonius’ biographies (Suetonius likes to collect gossip and seldom gives us analysis of events or even dates, definitely not public opinions on this matter) and writing centuries later we have Cassius Dio and Appian. Also none of these writers have an interest in saying what public opinion was at the time.
But Appian does say that soldiers of Octavian and Anthony were jubilant at the peace agreement. But the first thing that the Triumvirs did was order the deaths of 300 senators (including Cicero) and 200 equites. Furthermore the triumvirs also began to take money from the wealthy (mostly women and those they had ordered killed). But if you were not proscribed or taxed which was most people, I would believe that because the alternative to a triumvirate was a brutal civil war that would have disrupted trade and agriculture as well as cost lives, you would be pleased that peace had been made, if only temporary!