I do believe there are conditions where changes can be made to a set in reconstruction mode and the timers will be reset. If the adjacent buildings of a piece changes, the timer will reset.
Using the Cherry Garden set as an example. If the Gong of Wisdom was adjacent to two other pieces - Sakura Rock and Nishikigoi Pond - and this was changed in RC so that the Gong of Wisdom becomes adjacent to three other pieces - Sakura Rock, Nishikigoi Pond and Emperor's Entrance, then the timer would reset.
In addition, I believe that even changing which pieces are adjacent will reset the timer. If the Gong of Wisdom was adjacent to two other pieces - Sakura Rock and Nishikigoi Pond - and this was changed in RC so that the Gong of Wisdom becomes adjacent to Sakura Rock and Emperor's Entrance, then the timer would still reset. Even though Gong of Wisdom is still next to two pieces, they aren't the same two pieces.
Disclaimer: I have not tested this for myself.