Not sure if I'm following exactly what you're asking. On the p.c. in the Heavyweather program the actual data (text) screen will show the rain total since you first set it all up. This is fixed and resets will not clear this number. In the Heavyweather program on the main GUI page the rain total in the bottom right will show rain total since the last reset of this field (rain total). This amount is also shown on the station console in the rain total section.
An example of what I'm trying to explain. Since I first setup my 2810 back in Dec. 09, Heavyweather has recored and shows 127.83" in it's data screen since the station has been setup. I have been doing a "total amount" reset to the console on Jan. 1st to start off each year with 0. So right now my HW main screen shows 0.25" in the rain total (since Jan. 1st 2012) as well as on the console's rain total but in the HW data screen it still shows 127.83"
What gets uploaded to sites like Weatherunderground as total for the year is what is displayed on the HW main screen (0.25") not the amount in the data screen (127.83").
As for the 1hr. and 24hr. displays in the HW program, these fields also count down as their respective times run out. So if at 10AM it rains for 30 mins. and you watch the counts increase, this amount will also start to decrease exactly an hour (11AM) or 24hrs. (10AM next day) Maybe you saw the 2.20" in the 24hr. section midway in it's countdown?
Is this close to what you're asking or did I miss completely?