Tennessee raised 129 CS Regts & 56 US Regts
There were several refugee camps in Kentucky, Indiana, Ohio, and Indiana. Usually those with family ties in these states enlisted in those states units with their kinsmen. But with the likes of Andrew Johnson, WG Brownlow, Horace Maynard and others courting their constituants in exile were recruited into Units made up of designated Tennessee Union units. This was not unique to East Tennessee. The white union defenders of Ft Pillow were made up of Unionists from Tn, Ark, Ms, & MO. I continue to find an increasing number of former CS conscripts allowed to take the oath and enroll in Union regiments.
The following assurtions are from the DECLATION OF GRIEVVANCES ADOPTED AT THE GREENVILLE CONVENTION 17 June 1861:

Stated: "We prefer to remain attached to the government of our fathers. The Constitution of the United States has done us no wrong. The Congress of the United States has passed no law to oppress us. The President of the United States against the law-abiding people of Tennessee. Under the Government of the United States we have enjoyed as a nation more of civil relegious freedom than any other people under the whole of heaven. We believe there is no cause for rebellion or secession on the part of the people of Tennessee."
Suspecions were raised in Greeneville when the Memphis Appeal reported that 5,613, voted for sucession and only 5 voted for Union. No effort has been spared to deter the Union men of East Tennessee from the expression of their free thoughts. The penalties of treason have been threathened against them, and murdering and assissination has been openly encouraged by leading secessionist journals. As secession has thus been overbearing and intolerent while in the minority of East Tennessee nothing better can be expected of the pretented majority.
...the people of East Tennessee have declared their fidelity to the Union, by a majority of 20,000 votes (about 4 to 1)
As I recall There were about 335 signers at the Greeneville convention Only about 30 survived the war.
Union regiments raised in the south and designated by state as Union regiments was not confined to Tennessee.
Al, 6, Ark, 17, (I've seen that as many as 4000 men deserted Hindmans command after Pairie Grove and join the Union Army) Ga, 1 Fl, 2, Miss. 10, NC. 8, SC. 5, Tn, 56, Tx. ukn, Va. 1. Md. Ky. Mo., ukn.
There is a lack of clarity on whether, these states also included contriband units. La had at least 5 regts of Arty of African Decent as did SC. A stereo-type is that slaves were field-hands. However: a large portion of skilled slaves were stevadores and their knowledge of levers and pullies made them ideally suited for heavy artillery.
I had 3 ggf's in the war they grew up with in 30 miles of each other. 1 served the north, one the south, and one on both sides.