Select your objects. Then Object>Flatten Transparency. (Move the slider all the way toward vector.) Ungroup. Select the individual oubjects and check their fill colors. You'll see that they are tints of the spot color.
However, since this is a one-ink job, there really is no need to use a spot color. You could simply do the design using Black and tints of Black. What determines the color in a one-color job is simply the color of the ink that is loaded in the press (in this case, the silkscreen).
You have another concern, though. As soon as you incorporate tints of your one spot ink, you necessitate some kind of tone screening in order for the screen printer to reproduce the design. In other words, even though the design uses only one ink, any areas that are not filled with 100% of that ink will have to be converted to dots (or lines or a pattern) that is course enough for the silkscreen to hold.