Tasks are no longer automatically moving to 'Today'

Hi @Dawid_Wrzosek and welcome to the forum!

You are probably seeing the result of the updated My Tasks that Asana is just now rolling out. In lieu of the built-in auto-promotion, you can now create your own rules to define your own customized auto-promotion behavior.

For more on this new My Tasks, see:

I also recommend you read this article for additional help: