Bryan,
Are you now required to use only multiple timers? If so, what in the world is your instructor trying to teach you? How to do torture?
Generally in PLC programming, it is considered desirable to find shorter more efficient methods to do a job, not more complex convoluted ways. In a job enviroment you are not rewarded for finding the most time-consuming, inefficent way of doing a task (unless it is a government job)!
That said, if he wants "multiple timers", I suggest using all RTO (retentive) timers, with the firetruck switch stopping ALL timers, so that whichever one is active gets stopped in its tracks, then at the end of the cycle, resetting all timers with one reset rung (several resets in parallel, one for each timer). To do this successfuly and without problems, you need to fix your timers into a true cascade loop. The loop must not have "holes" (discontinuous parts) in it, otherwise the logic will become so convoluted as to be a headache for any poor electrician trying to troubleshoot or do maintenance on the system. In the real world that is a major consideration.
When the firetruck switch is off again, then whichever RTO timer was in control will resume where it left off. Because you don't know which timer will be energized when the firetruck arrives, you must interrupt ALL timers with the firetruck switch.
Let us know if you need additional help with this.