The problem with answering this question is that SimCity displays so little of "behind the scenes" information that it's basically been up to the community to decipher what's going on behind the scenes. Region play and Region statistics are disjointed like you say, probably because its also very slow to update.
Maybe part of your problem is the job requirement of 100% industry + 100% residential/commercial hybrid probably is too much for your 100% residential. Having a 33/33/33 slice of each RCI won't work in a single city so it wouldn't work in region play. Unless of course you zone high density residential and medium/low industry. If you zone high density commercial or industry you are screwed. This is due to a bug that High Density residential units can't keep up with the jobs that High Density Commercial/Industry creates. This is a well documented bug. Here's a link to the statistics on jobs:
Keep in mind that your game is only registering what each city sees of the region at the time.
1) When you load your Residential city: it sees that there are jobs in 2 other cities. I assume the Sims just commute to the closest city (just like they do in a single city). So all the residents just look for the closest job and come back. Why this city would have unemployment is beyond me.
2) When you load your Residential/Commercial City: it doesn't really care whats going on in the Industrial city as freight is not required, all it wants is those residents coming in to fill jobs, but it has residents itself. I think what's happening in this city is too self-sufficient. In other words maybe the workers never need to commute out because they have enough jobs in this city. By the way, the "commuting out" statistic (as far as I know) only counts as residents leaving your city if you have residential there. It won't count people leaving work to go home, or leaving a shop to go home.
3) When you load your Industrial City: it needs commuters to fill the jobs as well as Commercial to "ship freight" (which doesn't even work right). As you say its lacking workers, which I cannot explain if you have enough workers in those other cities. Pull up your statistics sheet and look to see if available jobs is more than available workers in your Residential City.
If you actually made perfect amounts of I, C, R cities, while you are loaded into each city, your other cities are frozen in time. All the Region does is count amount of Workers, Shoppers, etc in your other cities based on when the last time you played them was. I have used this frozen fact to my advantage by basically creating a minus income city that is producing absurd amount of power, water, etc to pump to my other cities. It doesn't matter that the city would go bankrupt in 1 month because unless you are LOADED into that city, time stands still.
There is several issues with getting perfect synchronization regional play right as you are trying to do, and I tend to avoid it since its buggy. It causes stupid amounts of traffic from the highway which can congest a city and bring it to its knees.
Like what was mentioned in the other thread you linked, its a very hard thing to answer what exactly is going on behind the scenes, but hopefully I gave you a few things to think about.