Greetings.
Today i installed boinc on my new pc and noticed strange behavior.
When i exit boinc program, tasks which i am computing not stopping and still running on background (i can see processes in task manager and they consuming cpu resourses).

Is there any way to fix it? Situation looks really annoying...

I think there is nothing broken, so also nothing to fix.

You probably exits the BOINC Manager, what's not the same as BOINC.

In BOINC Manager you have 2 options to end also BOINC:

1. In Advanced -> Shut down connected client
2. In Tools -> Options -> Enable Manager exit dialog

The first time you try and close BOINC manager, it should ask you whether you want to also close the client, or just the manager. There's also a "don't show this again" checkbox; perhaps you overlooked this? Easy to do in a world of pop-up dialog boxes.