Good question! The biggest issues with armies in the First Century was actually focused around it. I'll go ahead and answer your question early before going into a bit of a discussion on it :) The Marian legions were paid by their general, hence Crassus' line of: "A man cannot call himself rich unless he can afford an army." The system persisted throughout the First Century until Octavius/Caius Julius Caesar Octavianus/Caesar Augustus reformed the Roman military and centralized it...on himself.

One of the largest issues with this system was something we don't really think about in the modern lens. Previously, Roman soldiers were required to be landholders and their military service was just that: Service for the good of the state, which they had a vested interest in. By the time Marius came along, there was a massive shortage of landowners, and the Senate refused to allow him to recruit an army from the miniscule number that remained - so he took his plea straight to the poor and the unemployed, also known as the capite censei - the head count. He told them that he would pay them, he would equip and train them, and he would give them a land settlement after their term of service was completed.

Needless to say, these men who were struggling to feed themselves were delighted with the opportunity. They flocked to Marius, and he led them on a (relatively) successful campaign in Numidia in Africa, and then went up to the Alps to fend off a couple of invading barbarian tribes, who had been smashing through other, more conventional, Roman armies. He was lauded by the people, and he settled his veterans on some really good land in North Africa. This would become important within just a few years.

These private armies became extremely popular, and Rome was able to 'win' the Social War with them. The darling of that war, one Lucius Cornelius Sulla, was promptly offered a command against Mithridates of Pontus, an extremely wealthy region. While the Social War had gone on (The Italian allies rebelled against Rome), he had seized the opportunity to "free" Greece and the East from Roman domination - and Rome could not let such an offense stand. So Sulla raised a personal army to head on over. He gave them the standard promises of pay/loot/land, and had them all gathered and ready to roll. But then Marius, who was an old asshole at this point, had one of the tribunes veto Sulla's command. Marius was 'officially' put forward to replace Sulla. The problem? Sulla had an army, and that army was rather peeved at the news of their commander - and the loot/pay/land - being snatched away from them. So they "forced" Sulla to "unwillingly" march on Rome with them to correct the wrongs which had been enacted.

This was the first time a Roman army had attacked Rome herself, and the citizenry panicked. Marius fled into exile and Sulla used the presence of his soldiers to strongarm votes. They weren't only soldiers anymore - they were his greatest political asset, and they ensured he got what he wanted. In Sulla's case? It was just this command that he wanted (this time). But Marius, who'd coincidentally run off to Africa, wanted more. So Marius snagged all of his old veterans from their homes in Africa (they were apparently bored with farming), and marched on Rome himself. He completely overthrew the political system, having himself installed as consul and a lackey as co-consul. He had his enemies murdered in the streets, he ensured that the Senate wouldn't speak a word against him, and he basically took over the city. Sulla, once he heard about this, made a quick truce with Mithridates and headed right back to Rome, where he basically did the same thing. Kicked the Marians out after a bloody civil war, established himself as the ruler of the city, and executed a whole bunch of his political opponents.

This was the start of the first century BCE, and armies continued to be privatized and used for political gains until Augustus defeated Antony at Actium. The troops would fight for their generals and were loyal to the promises given to them by those generals - not to a greater sense of "Rome" or "country." The Roman state had never done anything for these men, while the general in question had offered them their dreams. They became the clients of those generals, and the generals, who were all politicians, took advantage of that to the best of their ability.

Hope that answered your question! :)