Revert "Revert "Let IME#onFinishInput called without dup onStart..."

Revert^2 "Verify lifecycle test when screen on/off"

c2769e41ea17d7f0d261396d28ddde3563422701

Reason: Fix forward Bug 174512702 and Bug 174445559
        with CL[1].

CL[1]: Icf1504d40b25fc5f53eae65d4bab48a3070db1d6

Change-Id: Id4e71a822bfde5fe6a263bbe094c0d238017efe1