Hi Mark, I'm curious which 5 in 1 (Iris) unit you have and how you connect to the internet.
I have a 5in1 that I purchased back in 2016. I really enjoyed it so year later I bought a second one to get another display (and have some spare parts, which so far I haven't needed).
I connect to the internet via an Access. My displays only receive information from the 5in1 outside, they don't send any information or get any information from anywhere except the 5in1 outside.
The indoor temperature is local to each display and since one is upstairs and one in the basement they're usually different. I won't see these indoor temperatures on the My Acurite app because the display is a read only device, it doesn't transmit any information only receives from the outdoor unit.
In order to get indoor temperature information I purchased some additional sensors. I have a temperature sensor in my office upstairs, one in the garage, one in the coldest part of the basement and one the reads the furnace output temperature. I also have one in the basement that does temperature and detects moisture at the low point on the floor(we had the basement flood once, not something I want to repeat).
So with my 5in1 system, I get the outside temperature and humidity (all the temp sensors have humidity too), wind speed and direction, rainfall rate and total, barometric pressure, AT MY HOUSE. I also have all the indoor sensors I mentioned above available in the app.
The ONLY information that the My Acurite app doesn't get from your own weather station is the very general conditions; light snow, partly cloudy, clear, whatever. Mostly fluff, the sort of stuff you can see by looking out the window. I hope that helps explain a little better how things work and why having your own station is better than something like the Weather Channel app.