Huh, I've tried several things and in the end I had it working as expected:

• removed patrol path and tilt presets and recreated, switch off/on all the related settings -> didn't fix
• reset the device via physical button and added the camera via ios app again (on wifi) -> same, didn't fix
• tried adding a microsd card, just to give a try -> nope 
• reset the device from VSM and added via VSM on ethernet and I've set presets and patrol path only there first -> worked, the patrol goes and if there is a movement the camera tracks, if the movement ends it goes back to patrol path, as expected

After that I've added the camera via the ios app as well, changed the network from cable to wifi, the patrol functionality remained well. So I'm glad with that right now. Thank you very much for your tips on trying to configure purely from VSM side. I don't know why works differently on the app.

Other thing, slightly connecting to the topic, the track movement is very sensitive and I can't see any option to change it's level. There is a setting for motion tracking events but that feature is for turning on alarm, getting notification or starting recording and doesn't change the PTZ tracking behavior. It's a pity if it can't be changed as a small movement on the surveillanced area (e.g. a bush or tree) immediately triggers the camera to move.

This is quite non-related but I've tried human tracking instead of movement tracking (because of the too much sensitivity as described so I gave a try) but it never gets triggered. Seems like not working at all. I've read that the positioning and lighting is crucial here but the camera position was fine and I was walking in front of the camera further and closer as well but nothing. It's also not triggering an event when I switch on the dedicated smart event function which means similarly not working for tracking nor event triggering. (sorry if I need to rise a new topic for this last thing, I'll do that if it would be the proper way.