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

This is a no-brainer. Tubes are going to be more influential because they introduce harmonic distortion, whereas cables do not.

I start with cables, aiming to achieve smoothness and liquidity—not necessarily warmth. In my second rig, which is already on the warm side, I was able to reach that goal using the Veritas Argentum XLR cable between the DAC and integrated amp.

However, in my first rig, which is more bright side of neutral, upgrading cables alone is not enough. While it does improve smoothness, it doesn’t fully get me where I want to be.  I’m now looking into tube buffer or tube preamp options.

It's hard to say without knowing what your base line is.  Both the cables and tubes have to sound good together. 

My experience with inexpensive cables is that they often soften the upper frequencies.  If you bought tubes that worked with them, you might not like those tubes when you upgrade to a detailed and neutral cable. 

I've played with a lot of cables and tubes to find the right mix for my system. 

Tube differences can be easy to discern. It depends a bit on whether you start off with basic OEM tubes, or whether you roll between various third party tubes. Upgrade from basic has been instantly recognizable, in my experience. Third parties may or may not be discernible. Some are also more a question of flavor, and preference may depend on what recording you play. As I listen to a wide variety of music, if any piece of equipment does not make all music sound better, then the it does not matter. I do not keep separate sets of tubes for baroque strings vs. EBM and switch them accordingly. And there is the habituation factor as well.

I have yet to hear any difference in any cable. Yes, I tried, and no, I have not heard any difference ever.

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.