How did they actually conduct the test? How long does it take?
In general, the opiate to be tested would be included in the assay solution, without the morphine dehydrogenase (MDH). This solution would be allowed to stabilize (1-2 minutes) so that a background signal could be determined. The morphine dehydrogenase was then added, and the peak response was measured after 2-3 minutes of reaction.
A typical resultant plot is shown here:

(from Peter-John Holt et al., Bioluminescent Assay for Heroin and Its Metabolites, Anal. Chem. 1996, 68, 1880.)
The brief spike in the initial stabilization period was observed for blank, control, and test samples alike, and was assumed to be a mixing effect only. Upon addition of the MDH, the luminometer response can be seen to increase, indicating that light is being emitted, and that a reaction (use 'back' if you click on this link) is occurring. The stronger the response, the more opiate was present in the sample.