The SCU did not make Caesar a hostis. That had come a few days earlier, on January 1st: Curio, fresh off his chaotic time as tribune, had run to Caesar and was back in Rome on January 1st of 49 BCE with a letter from Caesar, in which the general proposed to disband his armies if Pompey did the same. Lentulus, the new consul, refused to let the letter be read to the senate, but the new tribunes Antonius and Cassius insisted. The letter also suggested that if this final gesture of Caesar were to be dismissed by the senate and by Pompey, he "would come quickly to avenge the injuries done to his country, and done to himself." He did not need to specify that it would be with his 10+ battle-hardened legions.

Lentulus refused to allow any sort of debate or vote on the contents of the letter, and Pompey of course was not present in the meeting (he remained outside the walls to retain his imperium). Meanwhile, Metellus Scipio proposed that Caesar be named hostis if he did not disband his armies and quit his province by a fixed date (we don't know what). This was immediately vetoed by Antonius and Cassius.

The SCU came on Jan 7th, that the consuls, praetors, tribunes, and the "proconsuls near the capital" see to it that the res publica not come to harm. There was no specific language towards Caesar, but that last bit ensured that Pompey (with imperium) could "legally" begin to take direct action against Caesar. Cicero, who had arrived at the city on Jan 4th and who was also lurking with imperium outside the walls, but unwittingly and unwillingly caught up in the SCU as well and wound up being assigned to Campania to raise troops. Until this moment, Caesar had not taken any overt action against the res publica, and (probably rightly) argued that his legally-voted imperium was being curtailed and his legally-voted exception to stand for the consulship in absentia was being violated. In his eyes, the actions of the senate were illegal, and what came next only confirmed it: when Antonius and Cassius tried to veto the SCU, they were told plainly that their presence in the capital was no longer welcome, and their safety could not be ensured, sacrosanctity of the tribunes or not. They fled to Caesar and from what we can tell, he made the decision to invade immediately upon their arrival to him (about 10 January, though we don't know exactly). Only then could the senate really label him as hostis.