Assuming it behaves like its smaller brother, the SQ series, what you describe sounds normal, as long as the shutter actually makes an exposure. Unlike a typical 35mm SLR, the reflex mirror does not auto-return. (Assuming it's working) when you press the shutter button, the shutter closes, the mirror flips up and the internal film shutter opens. Then the shutter opens, and controlled by electronics in the body, remains open until the set time, then closes. As you describe, the system is mechanically reset by winding the film to the next frame.
So I guess the $64 question is -- does the shutter make an exposure? You might waste a frame at a 1 or two second shutter speed so you can actually see the shutter operation (if it works). In the SQ and SQ-A, a dead battery results in the maximum shutter speed (1/500) which is not very easy to see. There should be a button somewhere to do a battery test.
That's my 2¢ at this late hour ...