SOLVED
Alright, I found the solution!
Turns out i3
and mate-desktop
and/or caja
don't go well together.
After I removed both mate-desktop
and caja
, everything works fine now!
This explains why on Solus Mate Edition (that I used for testing) the problem is already there just after a fresh installation without configuring anything. So maybe this is interesting for the Mate maintainer.