Time tracking 101, you should never allow two time trackers to run at the same time (especially if you are planning on tracking and billing your time on a project funded by the government). Starting a timer should always stop all the others.
Good one - that sounds like great optional behavior. Having said that, I consciously built it this way. I personally use simultaneous stopwatches to track a full day of work and tagged items within that day, such as a specific meeting (each another stopwatch).
The "Personal Time" option subsequently merges the overlapping hours so that on Statistics, I'm looking at time spent in real life (as a person), while still being able to zoom in on specifically tagged items.