Does using heart-rate really improve REM detection?

For my sleep issues, I want a trigger at the beginning of a REM stage.

The problem is not so much getting and using the trigger (I know how to do that), but that the SaA ~REM trigger most of the time does not come at the start of the actual REM stage (I know that ~REM is guessed).

The ‘How it works 6’ -> ‘Sleep actigraphy’ page says:
https://sleep.urbandroid.org/documentation/core/background

NOTE: In case only actigraphy is employed the ~REM figure in the graphs
is just an assumption based on and is not directly based on common
knowledge on sleep. In general actigraphy is not powerful enough to
directly recognize the REM phases. In case you use an additional heart
rate sensor we do REM phase detection on a the combined activity and
heart rate data (see Wearable)

So I bought a Xiaomi Mi Band 2 (and the Tools & Mi Band app).

The Mi Band 2 works fine with SaA, but I see no improvement in REM detection.

My references for my real REM stages are 1) notes (when I wake up after a nightmare) and 2) the sleep-graphs from my Fitbit Alta HR tracker.

I am under the impression that the REM stages shown by Fitbit are much more accurate than those of SaA plus Mi Band 2, but the Fitbit ones are useless for me, because one does not get that data untill the next day,
i.e. after the fact.

Does anyone have an explanation for the differences I am seeing or and any suggestions on how to improve the accuracy of the SaA ~REM triggers?

Thanks in advance.

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