Is your request then that you want to have the on-time and off-time always the same? Meaning, you want 1_second to be 1_second on Design#1 and also 1_second on Design#2.

Then you must get your reference clock as accurate as you need it (which is what has been mentioned before). This has nothing to do with locking oscillators or anything like that. You want watch#1 and watch#2 to always read the same, correct?

So your task is to determine what does "always read the same" means. If you need them to always be the same , with not tweaks whatsoever, forever and ever then you need to phase lock them - but this is not realistic for watches and doesn't look like it is for your application either. You then need to determine how much drift you can tolerate. Drift will happen, and you have to determine how to deal with it. Watch manufacturers (sorry I keep using watches, but it is an easy timekeeping tool) allow you to "tweak" (adjust) the time for that reason.

You can use a crystal for your reference and pay attention to the drift requirements. The higher the number the more it will drift. You could also look at an RTC to serve you as the "time-keeper". You still may need a means to "adjust/tweak" if you want them to start right-on.