It's kind of true. But your timing is off.

Violence in Missouri began almost immediately as soon as the Mormons started to settle in the area in 1831. They arrived with a revelation that said NW Missouri was "in the hands of your enemies" but that God would deliver it into the hands of the faithful. Arriving in a block the Mormons scared the hell out the locals, who knew about the violence promised in the Mormon scriptures. There were also cultural differences, most of the existing Missourians had immigrated from the Deep South, while most of the Mormons came from New England and Ohio. And the Mormons were proselytizing to both slaves and Native Americans. In 1833 it broke out into violence. There is no doubt that the Missourians started the fighting, but the Mormons returned violence for violence. But in the end the Mormons were badly outnumbered and were driven from Jackson County.

At this point Smith raised his first army, Zions Camp. This force of maybe around 200 men left Ohio in May of 1834 and marched to Missouri to force the locals to allow Mormons back to their properties. By all accounts it was a failure. It accomplished none of its goals, while ratcheting up tensions even further. It disbanded without ever having fired a shot. A compromise was later worked out letting the Mormons have Caldwell county, an agreement that in 1836 was even approved by the Missouri legislature. In 1837 Smith moved the church headquarters to Far West in Caldwell county.

Unfortunately the Mormons were never entirely contained in Caldwell. There were a number in Carroll and especially Daviess counties. Their presence again sparked violence in 1838. The summer of 1838 started off with a schism within the LDS church. A group of leading Mormons signed a manifesto telling the dissenters to "depart or a more fatal calamity shall befall you." By this time the church had grown a sort of secret society within the church called the Danites. They were something of a paramilitary group / secret police, organized to meet violence with violence and to enforce the word of the Prophet. There's disagreement about how closely they were tied to the leadership, and Smith at several times excommunicated members of the group. But in 1838 they were definitely on the inside, with clear ties to the church leadership. So the dissidents took the warning of fatal calamity seriously and fled out of Caldwell, and raised a lot of anti-Mormon ire again. In response Smith's right hand man Sydney Rigdon, gave an infamous speech on July 4th, which called for a "war of extermination... until the last drop of their blood is spilled." Needless to say, this didn't exactly calm things down.

So with that the Mormon- Missouri war started in Gallatin, in Daviess County, when a group of Missourian's tried to block the Mormons from voting. The local Mormons summoned the Danites and drove the Missourians off. Charges were filed. Countercharges were filed. Small fights broke out here and there. Militias were raised, and Missourians and Mormons alike began to raid each other's properties. Local authorities evacuated Missourian women and children from much of Ray county. The Mormons attacked and drove off the Ray county Militia at the Battle of Crooked River. This lead to the raising of a large State militia to "quell the insurrection" and the Extermination Order. Within short order the Mormons were driven from the state and their leaders arrested. To answer your initial question, the extermination order came after some of the violence, but before Smith ever had himself crowned king.

By the Spring of 1839 most of the Mormons were across the Mississippi in Illinois. By May, Smith escaped jail and joined his followers. Trying to avoid the mistakes of Missouri, they bought several large adjoining plats of land in an area that was largely unoccupied. Instead of settling in a series of small isolated villages, they flocked together in a single city, Nauvoo. Smith immediately filed for city charter that would allow a militia, and all the other trappings of government. This allowed Smith to raise his second army, and his first real one. The Nauvoo Legion at its height was around 2,500 men, and may have temporarily swelled to up to 3,000 at points. It had uniforms, a surgical staff, even a single cannon; and Smith was looking for more to create a small battery of a dozen or so. This was at a time when the US Regular Army had less than 10,000 men total. The US Army relied on these local militias and volunteers in time of war. It was a significant and by contemporary accounts well organized force, it eventually formed the basis of the Mormon Battalion in the Mexican American War. Smith made himself Lieutenant-General of the Legion, so that he was the highest ranking officer in the US and couldn't be court-marshaled.

He also got himself elected as Mayor, Head of the Municipal Court, along with remaining the Mormon Prophet. As court head, he made sure the Nauvoo courts were occupied by his men. He was thus able to quash the many extradition requests coming from Missouri and Ohio, as he was a wanted man in both states. As Mayor he was present for all city meetings and could sway the city council which was almost entirely his men anyway. At this point he was running a theocratic micro-state. He controlled all three branches of government and an army that was larger than the rest of the Illinois militias combined. However it should be mentioned that for most of this he was directed inward. He wasn't out to conquer; he just wanted to rule his people.

In 1844 he took a turn toward the megalomanialcal. The Mormons had been petitioning the federal courts, and the executive branch for the return of their Missouri properties. These had largely petered out. They found a lot of sympathetic ears. But no one was too eager to publicly take up the cause of a perceived apocalyptic cult. So Smith got the bright idea of running for president. He began to also receive revelations that told him he would become the leader of not only the US, but eventually the whole world. He had himself crowned and anointed as "King of the Earth." He also established what is commonly known as "The Council of Fifty," which was to act and prepare as a shadow government for when Smith took control of the US and other lands. Interestingly enough the Council was nominally non-denominational, and separate from the LDS Church, and included non-Mormons. The Council took a few official actions, including sending a delegation to Texas to try and convince Sam Houston to join The Kingdom of God. Another delegation was sent to Washington in an attempt to purchase Oregon for the same purpose. That didn't last long though. Within three months of the Council's founding Smith had been gunned down.

And that's a brief overview of Joseph's military and political actions. The man was certainly ambitious, and he had no problem using martial force to achieve his goals. He did have himself declared King. But there was no sign that he ever intended to use his largest army to achieve that goal. It appears that he expected it to happen through election and negotiation, and the divine intervention from God.

For general Biographies of Smith Fawn Brodie's older No Man Knows My History and Richard Bushman's more recent Rough Stone Rolling are considered the standards. Although both have their critics. Brodie for being a bit dated, and Bushman for being a bit too apologetic on Smith's behalf. If you are interested in any more specifics on what I wrote above, I would be happy to provided additional details and sources