Thank you to everyone that has helped me diagnose the problem!
Knightrider was able to confirm the behavior that I am seeing with version 3.228 that I downloaded from X10's website. There may be another version that corrects this problem, but it is not available to the general public. If anyone knows about this special version please PM me. Otherwise, the work-around that I have employed is to use dummy appliance modules to turn my lights on with a timer, and then I use a 2nd timer that turns those lights on with a lamp module so that the dim/bright levels are correct. If anyone else experiences this same issue and has any questions, feel free to post below or PM me.