All the Northern people knew at the tiem of Lincoln's assassination was taht a Southern Confederate did the dirty work, and in sewing the wind reaped the whirlwind to paraphrase Bomber Harris.

Whether the South wanted anything to do with Booth is immaterial. After having lost 300,000 people to put down what they saw as treason, they were in no mood to split hairs.

And I'll bet there were hundreds of thousands of Southern Confederates who cheered Booth's deed as a noble act of revenge. Or do you have evidence that most Southerners were equally outraged at Booth instead of clapping their hands in joy?