How can I use the 24VDC of a unit, if that unit doesn't supply 24VDC?
Well the fact that you are using the BX-DM1E-M
-D and the BX-DMIO-M
-D, of course, means you can't.

I installed a BX-08AD-1 here and tested it. Of course, mine worked as expected. With no +24VDC then I got the warning. With +24VDC, no warning. Also, by default, the 08-AD-1 is 4-20mA and will report "broken transmitter" with no connection. But if I configured it for 0-20mA, then no "broken transmitter" error.
The analog cards have the supply terminals inverted than what is normally expected. 0V is on top, 24VDC is on bottom. Are you sure they are wired up properly? And you are measuring the 24VDC at the terminals of the analog modules themselves? Because, otherwise, I'm running out of ideas. It should just work.