A reddish cast with E-6 could be the result of too high processing temperature.
I have no idea why the Ektachrome came out correctly and the Provia came out too red.

Maybe your Jobo drum is not perfectly horizontal, one half doesn't sit well in the water and develops "cooler" (Ektachrome) while the other is warmer.

At which temperature do you set the Jobo? How many minutes of first developer?

I have a Jobo CPP2 with "lift", I set the temperature at 38.3, the speed between P and 6.

In general Fujichrome film needs a bit more development time than Kodak (different thickness of the emulsion, or whatever).
The canonic 6:30 become 7:00 or even 7:30 for Astia.
You should develop Astia and Kodak film separately and, through tests, determine the correct development time in your setup for each film*.

The difference between 6:30 and 7:30 corresponds to around half a stop.

YMMV

* I know in theory E-6 is E-6 is E-6, but practice and theory sometimes diverge.