Yes, the spool should sit stationary on one end, and the wire will unravel itself around one of the flanges. Most winders mount the spool vertically, with the wire coming up straight off it. But it doesn't have to be vertical. In my winding rig, I have the spool mounted almost horizontal, tilted up about 10 degrees. I made a wooden holder bracket with a wood dowel sticking out. The spool sits on the dowel, and the wire feeds off the end, unwrapping itself around the flange. My guide/tensioner sits about 12" in front of the spool, roughly lined up with the dowel. I'm using the large 5 lb spools. For little 1/2 lb or 1 lb spools, it should be 6" or so. From there, on my rig, the wire goes forward another 8" then wraps around a Delrin pulley, which is the guide that mechanically traverses side to side. Off the pulley, the wire only goes an inch or less and it's on the bobbin. That's how I built mine, but you can arrange the wire routing other ways to fit your workbench.
The key thing is that you need to have some kind of first guide out beyond the flange of the spool, lined up with the center. As the wire unwinds, it whips around in a cone shape. As you wind at 1000 rpm and beyond, the centrifugal force can swing it around in a big circle if that first guide is too far from the spool. If swings around too wide, it can get tangled or caught. Some guys use a plastic funnel as that first guide, mounting it so the wide end is about even with the spool flange.
You can mount your tensioner device right there at the first guide, or further down the path. I made it all one unit, because I wanted to keep the overall wire path length short. You can see the general arrangement in these pictures. That's the spool in the background at the right.
Related tip: Always check the flange of the spool to make sure it's smooth all around. Nicks, cuts, or molding flash can snag the wire and break it.