but I don't think it could be the reason of this issue, because it doesn't explain why if you don't add any amp in pre, you can instead hear the effected sound
Sure it does. If you put an amp block before the effect, that's a dual mono block. That means that it's summing the two mono signals coming into and outputting two identical mono signals. So if you have wet and dry going in, there will be a wet/dry mix coming out.
I actually don't quite understand why the Analog Delay model behaves this way. The Boss DM-2, which that effect is modeled after doesn't have a separate dry out. The DM-3 does.
This is just one of the little oddities that appears because of the way Line 6 handles the stereo signal paths through these effects.
"It is not our duty to understand the arbitrary, meaningless dictates of machines"
- Don Norman in The Design of Everyday Things