Roman soldiers weren't some sort of homogeneous blob that all held the same opinions, nor were the members of the senatorial class or whatever. There were armies fighting on both sides, composed of soldiers loyal to their commanders' causes--or at least, willing to fight for them. Even within that, attitudes were extremely complicated as to drawing up sides and whatnot. Caesar had several legions defect to Pompey, and his most trusted legate, Labienus, went over to Pompey as well and commanded Pompey's cavalry at Pharsalus. Antonian legions defected to Octavian throughout Octavian's career, even while Antony was on Octavian's side, and Horace (who served as military tribune under the Republicans at Philippi) shows in his verse very mixed attitudes towards both sides. Such feelings of ambivalence were surely not uncommon. Other than the rather unhelpful and probably not very true statement that the troops that sided with Octavian or surrendered to Octavian were for the most part okay with allowing him to take control of the state (and even then, a lot of people who sided with Octavian were willing to back him up to put an end to the civil wars, or for all kinds of other reasons) there's really not much we can say about that.

That would be the end of that, but you've asked some other questions, so let me try to answer them as best as I can. The Praetorian Guard as a separate, codified organization was created by Octavian. Previously the praetorians were simply the selected troops of a general's bodyguard--every magistrate holding imperium had praetorians. The question of what role troops had after Caesar's assassination is hard to answer for the same reasons as your initial question--there were a lot of armies in existence after Caesar's death. Obviously there were the civil wars, but military forces held significance before the outbreak of actual war. Octavian could not legally command armies when he arrived in Rome, holding no magistracies, but built a force of private bodyguards using his own money (or, really, money loaned to him by his allies, since Antony refused to hand over his inheritance) composed mostly of Caesar's expired veterans. Octavian had several legions go over to him during this time and therefore illegally commanded an army--an army that would become legal when Cicero granted him an extraordinary magistracy to march against Antony at Mutina. In the course of the battle both consuls were killed, and Octavian became sole consul and was left in command of his own army as well as both the consular armies, which certainly helped him win a spot on the table when Lepidus approached him and Antony about setting up the Triumvirate.

I'm afraid it's not a very satisfactory answer, but your question isn't particularly easy (if even possible) to answer, at least not the way it's framed. So I apologize for that