There's almost no way you wouldn't understand that the issue of slavery could lead to disunion, it was an omnipresent issue that would have been known and discussed among every class of person in the entire country, not even just the south. Political news was a mainstay of newspapers, which regularly included commentary on political issues in the form of published letters and editorials of concerned citizens, and reprinted letters, speeches, presentations and essays by ex-slaves like Harriet Tubman and Frederick Douglass, as well as abolitionist preachers, and of course they also published speeches, essays, and opinions of those who supported slavery and called for secession.

As an example, a small newspaper from Ann Arbor, Michigan, wrote a lengthy article about John Brown's trial in its November, 1859 issue. The writer is unsympathetic to Brown's cause, but impressed by Brown's character. It includes discussion of numerous other interrelated topics and distinguished between republicanism and "Garret Smith abolitionism" the latter of which intended to "abolish slavery by insurrection, rebellion, civil war and human slaughter" rather than the former's "peaceable, legal, constitutional means." The article on Brown is followed by a second article summarizing a short speech in which the raid was blamed on the Democratic party itself, a result of their meddling in Kansas and the unambiguous federal support for the slaveholding elite in that and other conflicts. Obviously, few if any people in the south were reading a newspaper from Ann Arbor, but that such a paper - only 4 pages long - regularly included discussions and opinions of national politics from a perspective friendly to their subscribers.

Outside of newspapers, discussion of national political issues, including but not limited to Brown, the ongoing violence in Kansas and Missouri, the fugitive slave act, acrimonious and violent debates in congress, all variably factual, would have been conducted in churches, masonic meetings and other social societies, would have been the subject of speeches and sermons and letters and novels. Knowledge of an impending constitutional crisis - framed either as the complete federal submission to the slaveholding elite or, on the other hand, the violent conspiracy of anarchic abolitionists - would have been widespread and public, and it would be very unusual for even a poor farmer to not have an opinion about it all, and very likely a quite intense opinion, one way or another.

What would a poor farmer have done about it once war was declared? It depends. Some tried to maintain neutrality, but secession was widely popular in the south and initial calls for recruitment into the nascent rebel army drew a huge number of recruits. Since these calls were for volunteers, there would be no reason for a poor man to flee anywhere, as there was no draft as yet. Rural populations in the south varied politically from rather friendly to the federal cause to, obviously, violently opposed to it. Farmers could and often did sell some of their property to nearby armies (or were poorly compensated for when soldiers liberally "foraged" from their crop). There were, as far as I know, no large-scale movements of white southerners, but there were massive movements of enslaved people, who fled bondage to take refuge near federal outposts or to federal front lines during invasions. So many fled to Fort Monroe in the Virginia peninsula before and during the Peninsula Campaign that they raised a "great contraband camp" of self-emancipated former slaves who wished to place themselves under federal protection. Many offered services as laborers, scouts, spies, and soldiers, though the official recruitment of black soldiers had to wait a while.

In short, you'd probably understand the secession crisis quite well, at least from a perspective of your own sympathies and beliefs. Those beliefs would have influenced your decisions once the crisis turned into the secession and rebellion, as to whether you'd try to avoid it, profit from it, or volunteer to serve within it.