I'd like to quote the world expert on Actigraphy - Avi Sadeh:

There's no scientific evidence that REM state can be determined from actigraphy data alone
This means that the OP's point of waking up in REM on the basis of sound and movement is primarily due to luck and good timing on his part. That app would wake you up in "light" sleep stages, which may be anything! It may wake you up before REM, after REM or during REM. This is completely dependent on the kind of sleeper you are!