I was watching the data on this integration in HA today while it was raining, and while the precipitation_rate value does appear to be changing, and passing through to HA, as far as I can tell, rain accumulation is coming through as 0 for Tempest (obs_st), even when there is rain accumulation for the day (actively falling).
I think somewhere around here https://github.com/briis/pysmartweatherudp/blob/master/pysmartweatherudp/receiver.py#L209 you need a self.precipitation value to be set.