There is no source that clearly states Fulvia raised legions herself. The closest is Appian, who writes that she "urged Ventidius, Asinius, Ateius, and Calenus from Gaul to help Lucius [Antonius, brother of M. Antonius], and having gathered another army, she sent it to Lucius under the command of Plancus" (BC 5.4.33). He does not elaborate and is, in general, a lousy source, especially for specifics. If your only mention of (x) is Appian, you are on very shaky ground indeed. On the other hand, the rules and mechanics of how raising legions worked, even in the chaos of the triumviral period, is well-known: only individuals with imperium (legitimate or otherwise) could raise legions.

The trope of Fulvia as "mannish" and displaying male qualities is familiar from many sources, most of which are clouded by Octavian's very forceful propaganda on the subject. Marcus Antonius' rival was very interested in pushing the idea that he was weak and dominated by those around him, particularly women. Fulvia's reputation as a "pushy" woman went back to her relationship with her first husband, P. Clodius. Valerius Maximus, V. Paterculus, and even Cicero make off-hand references to Fulvia as mannish or militaristic. Plutarch, famously, has this to say:

She took no thought for spinning or housekeeping, nor did she deem it worthy to have power over an ordinary man, but she wished to rule a ruler and command a commander, so that Cleopatra was indebted to Fulvia for teaching Antony to obey a woman’s nature, since she took him over accustomed and trained to listen to the rule of women (Vit. Ant. 10.5-6).

The Appian passage above, then, when viewed from within this narrative of Fulvia as a "pushy" lady, as a meddler, as over-stepping her bounds. So here in Dio:

"Lucius went around everywhere, banding them together and detaching them from Octavian, while Fulvia occupied Praeneste. She was accompanied by senators and knights, and having set them about her as a council, she deliberated with them and even sent orders to wherever they were needed. And why should anyone marvel at this, when she would gird herself with a sword, give out the watchword to the soldiers, and many times, even speak to them. All of this gave offence to Octavian (48.10.3-4)."

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Now, with the problematic sources taken into a count: could a woman operate in this way in the world of the (very) Late Republic? In theory, yes. By this time, soldiers had begun to follow their commanders rather than their senate and people, and had already ignored the wishes of the latter on dozens of occasions over half a century of conflict. If Fulvia was half as forceful and competent as the hostile sources make her out to be, there is no reason to believe that soldiers loyal to Antony would not allow themselves to be directed by her, especially in the upper echelons.