Time offset only works on objects that are
directly animated! For example on the growing vines, they grow because the taper object is animated with empties/ hooks. So applying timeoffset to the growing vines themselves does nothing because they don't have an IPO, the hooks on the TaperObject do. So for example if you want the vines to start growing at frame #25 then you type 25 in the timeoffset of the empty/hook that animates the taperobject curve. I shoulda been able to figure this one out quicker, sigh
Note: TimeOffset is in the AnimSettings Panel in the editing panel