The watering process will not be stopped because of rain unless you have a rain sensor installed.
Rachio looks at the weather report for the day (say at 1 am) and determines the watering needs. If it determines watering is needed for today (forecast shows little or no rain) then that program will run, even if a monsoon hits.
Tomorrow at 1 am, Rachio again looks at the weather yesterday (rained) and the need today, and determines if it should water.
The program if flex daily and not synchronous live tracking.
Although re-reading you post, I see it was in fact yesterday's rain and not today's that you were posting about. So perhaps the accumulation was not updated to the web for access. Sorry.