And the fact that Lincoln blockaded the late-joining border states, itself an act of war, before they even voted to join gave many of them good cause to do so.
Lincoln's executive order was issued two days after Virginia seceded and only mentions the states which had already joined the Confederacy. Nor would Tennessee or Arkansas be affected by a naval blockade. How the blockade was enforced is another matter, but if there were property seizures and fighting already going on, one could understand why the navy might also apply it to Virginia or North Carolina. After Sumter it was clear to all that states that voted for secession had cast their lot with the Confederacy, so the blockade might have been extended to them. But I've seen no evidence for this. The news that the Confederate states were to be blockaded had an effect on opinion in the Upper South. But all the evidence I've seen is that the blockade that Lincoln declared extended from Texas to South Carolina, and did not include Virginia or North Carolina.