Does this mean that the Inoveli Aux switch won’t work in these configurations?
No. They will all work.
OK, great! Thanks for confirming 
Inovelli Aux DOWN doesn’t turn-off light, but Aux SCENE does. After some time, the light begins flickering and then the DOWN button on the Aux starts working.
UP: paddle button that normally turns lights on
DOWN: paddle button that normally turns lights off
SCENE: small button beside paddle
It’s a bit like this. I’ll check if any of these solutions work.
have you confirmed that the switch is set to 3-way with Aux?
Yes, the switch is set to Multi-Way Aux.
The LED flashes cyan and yellow after turning-off the lights.
This sounds like the switch is rebooting. Double-check the switch type for 3-way with Aux, but the could be a wiring fault, either miswiring or a loose conductor.
Thanks, the switch is already set to Multi-Way Aux, so I’ll check the wiring. I’m wondering if it could be something like this.
What is the load on this leg?
The load is recessed lights with regular LED bulbs.