Trump was noting that Jackson would not have tolerated the secession of the first Southern State, something that James Buchanan, president at the start of the conflict, allowed. Lincoln's election may have laid the charges, but it was out-going president Buchanan who let the initial States secede and seize US forts within their borders. As Buchanan said "The power by force of arms to compel a State to remain in the Union," was not among the "... enumerated powers granted to Congress."
Jackson may have been a slave owner, but he was also a man of action and a patriot. When the State of Delaware passed a law effectively disbanding the State militia Jackson threatened to arrest the legislature (since he as commander in chief commanded that militia). He fought some of the most prominent politicians and business men of his time, taking on even the Supreme Court. Call him an imperial president if you wish, but Jackson would not have sat on his hands as Buchanan did when South Carolina Seceded in December of 1860.
Now would Jackson have ended Slavery, Its pretty obvious he held with the institution. But while in office as president he made no attempt to roll back the ban on importation, or the Missouri Compromise of 1820 which had prevented Civil War back in Monroe's presidency. At the same time he did sign the 1830 legislation forcing the removal of the Cherokee indians (who had declared themselves an independent nation in 1927).
And he was a believer in freedom of travel. In 1811 Silas Dinsmoor, Indian Agent for the Choctaws got on the bad side of Andrew jackson when he ordered enforcement of a law that required anyone traveling the Natchez Trace through Choctaw territory to carry papers with them proving their ownership of any enslaved people accompanying them. It was an old requirement, just as freedmen were required to keep the documents attesting to that. For Jackson, who used the Natchez trace to move goods from Nashville to Natchez when the river was low, it was an unacceptable requirement. Exactly when Jackson threatened to arm his slaves and then to burn down the home of Dinsmoor (after hanging him) is uncertain. But the war of words matches the time when Jackson was marching his troops back to Tennessee along the same Natchez trace. And one would expect Jackson had a few servants with him on that march where he gained the title old Hickory.
In short Jackson was a man who didn't tolerate things. He fought duels, and threatened to hang others (Dinsmoor wasn't the only one). As stated he ignored the Supreme Court Justice Marshall and yes, he threatened both the State legislature of Delaware and of South Carolina (who was implementing Nullification). And in all cases, prompt action on his part stopped things from advancing further.