Okay, guys. I did some tests. To be perfectly honest - nothing helped. I still get those leaks, even without any mixer connected to my Helix at all.
I have double checked my connections, DAW routing, cables etc. Whatever audio is sent from Reaper to Helix Output 1 ends up being played through my guitar cabinet. On the contrary, Helix Output 2 is completly flawless.
Maybe there is something wrong with my setup that I can't see, but for you it will be obvious. Here is how I routed everything in Helix.