In my old controller, I had an external sensor that would physically sense the rain, then my controller would delay until the sensor was dried, usually three days. This week we had 4.5 inches of rain over 5 days. Everything is green and saturated. The Rachio did skip/delay (Not sure) during the rain. But after 1/2 inch of rain Sunday morning, Monday was skipped and the controller started watering again Tuesday morning. I have the smart weather sensor turned on. I would expect a longer skip/delay time.
What schedule are you running? Fixed, flex monthly, flex daily?
I just checked and I have fixed. I have to schedule on specific days in my town. So I deleted that schedule and created a Flex Daily for Tue/Thu/Sat. I supposed these days will be skipped if enough water?
Full transparency…just switching to Flex Daily, especially with watering restrictions could be a gamble right off the bat. Are you confident that you have all the parameters set up correctly in Rachio (soil type, crop type, and nozzle PR are probably the most important). The restrictions could cause you to see some odd behavior as the schedule looks ahead to plan for future watering knowing that it is limited.
What Flex Daily does give you is the ability to see the moisture graph, which allows you to see what Rachio thinks your yard is doing based on the algorithms and the data you input for the zones.
I agree about Flex Daily considering the 3 days a week restriction, but other than Flex Daily, no other programs total water received. Six inches of water one day will prevent watering that day, but a day or two later, watering will be back to normal, which is what I think is happening to the OP.