Ok, it works now !
1 - First, DTR has to be pulled HIGH before pulling it low OF COURSE !
So to "manually reboot the ProMini trough DTR, I first had to pull it HIGH with a 10KOhm resistor
2 - The on-board capacitor seems to be a little bet low and it doesn't work all the time. So adding a 2nd 0.1uF capacitor in parallel with the original one make it working any time I pull DTR down.
So, that way, I could verify that my ProMini DTR pin was "manually" able to work. That was the first point at least.
But it still wouldn't work with the "CP2102 USB to UART Bridge".
The thing is that the "CP2102 USB to UART Bridge" is on 3.3V and my ProMini on 5V (The ProMini has an on-board K50 regulator, I checked it). And of course connected together, the DTR pins were hold HIGH at 3.3V, not the 5V requested for a proper pulse.
Fortunately, my 5V ProMini seems to be able to work fine on 3.3V. So I fed it on 3.3V instead of 5V so the DTR pulse would be a nice straightforward .3.V HIGH to LOW level but it WORKED fine any time this way !!!
Any remark welcome.