I did investigate a bit more what happens when and under what circumstances.
My conclusion is:
It seems to me that the unprecise time is taken from the gps-module of the rapsi.
The more I place my antenna to a “better” spot, the more accurate the time is.
If this really is the reason, how am I able to change the chirpstack to use the systemclock to provide a more accurate time in the mqtt-frame?