Well, to sum it up. I removed all calls to Update(0) and refactored these places to with better understanding what Spine is doing. So it is not a black box anymore for us. Thanks for helping me with that! Now a lot of things seem obvious, but e.g. playing empty animations for proper mixing is nothing easily understandable.
And still, I found a runtime bug
Next time I will directly try to isolate and understand what is going on instead of quickly hacking it with Update(0) call.