I have created a new *.ahx file. This time the modules in the software responded a little bit differently, but the hardware response (and no response) is exactly the same.
Initially the modules would simply go from off/full dim to off/full bright when they were supposed to turn on. After I selected the "issue on instead of bright 100%" option, the modules showed that they went from off/full dim to on/full bright. The problem is that in both cases, the light never turned on. If I click on the module, it turns on, but the timer does not turn the light on.