Question about intertechno Radio universal dimmer ITDM-250

Switching via light switch and remote control always works regardless of which you last used, provided you connect the module correctly. If you have a dimmable lamp/bulbs, you can dim the lamp both with the remote control and by "double-clicking" on the light switch. The module then takes over this function.

The remote control always works, as does the light switch. There is permanent power on the module.

If installed correctly, both will work.
The conventional light switch no longer connects the mains voltage but only a control contact of the dimmer.
This means that the dimmer remains permanently connected to the mains voltage.

Yes, the dimmer switch works normally.

But then you have connected the dimmer incorrectly. The switch is completely disconnected from 230V and is connected to the 2 white wires of the dimmer. How the switch and remote control work

Hello
The assumption is correct.
If the dimmer (with remote control) comes after a switch, it is correct that it is dependent on the previous switch and its switching status (on / off).
Does this answer the question clearly?

There's no problem, the remote works to turn the lights on and off even if they've been turned off with the switch.
Personally, I use a Jbmédia module and I can control my lights directly from my smartphone or tablet.