The new version adds “Pulse mode”, which speeds up the time in the game without changing the time on the system clock. No manual manipulation of the watch is required. Technically, the clock translates to 59 seconds. back, and in a second 60 forward. Of course, something may be buggy in the system, but visually you always see the exact time.
Tested on Fallout Shelter 1.61 – Works! Source code attached.