Do you start fine tuning the system with cables or tubes ?

Tubes in most cases. 

Tubes definitely make a more discernible difference in my experience.  The biggest impact I have had with tubes are 6SN7 and rectifier tubes. I could not believe the difference a Mullard GZ34 made to my system after inserting it into my Allnic phono power supply.  It was akin to a component upgrade.  

I have also owned and tried a ton of cables. not as impactful as rolling tubes, but more of the final seasoning to the soup. The system and the room need to be addressed before dropping large sums of investment in cables IMHO.

Yes, assumption is that both the cables and tubes are already quite good. That's why I called it fine tuning, your system is tuned but you want to take it a little higher without changing active components.

In my case, cables are excellent and I don't think about upgrading them because it would make more sense to upgrade analogue front end and speakers before doing it. So I proceed with tubes, though here too I believe I have found the right balance for my VAC Avatar SE integrated. One could do better but at high cost.

Neither. Your system should sound good with stock tubes and basic, well  designed cables. If something doesn't sound right, fix the problem. Using tubes and cables to fix a problem is almost always a bad idea. Once you get everything sounding OK, different tubes an cables can be used to enhance an already good sounding system.

In my modest but very revealing system I started with the entry level cables I had (Zu ) . I rolled tubes in my pre and power amp. I went to Anti-Cables and rolled tubes again. I then went to Morrow level 5 and rolled again. Please keep in mind that almost ALL of the tubes were purchased in the beginning. Also @hilde45 pointed out room treatments are paramount. Part of my tube rolling was to accommodate for room acoustics, which would be unnecessary if my room was treated properly in the first place. Happy Listening, Mike B.