It is extremely unlikely that accurate measures of sleep will show "REM sleep before deep sleep" and I would be very suspicious that this is an artifact. Accurate sleep staging requires measuring brain waves and no home device measures this directly. You are most likely using a home device such as a watch that does not actually measure REM but but substitute markers for REM and all of these have substantial errors. You cannot really rely on the information to be completely accurate. In general REM sleep is highest in young people and mostly iseen in the second half of the night. Feeling tired in the morning probably has nothing to do with REM but has many possible causes. Sleep deprivation is of course a really common cause. Drugs, alcohol, caffeine, irregular sleep and wake patterns and things that disrupt sleep will lead to morning sleepiness.

Fit bit is not a reliable modality to pick up REM sleep .REM normally occurs within 90 minutes of sleep onset . And occurs every 90/120 minutes with significant portion occurring in first of night .
Deep sleep may occur later and is usually about 25 percent of your total sleep