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

Room acoustics is top priority. Unless that’s shorted out you are not really hearing the potential of your components. 
Properly treated room will also reveal differences between cables, tubes and even masters of the same album much easier. It will reveal any inconsistency in performance of your tubed equipment on a day to day basis. You will be rolling tubes endlessly because tubes will be the first thing you will always suspect when the system sounds off. Eventually you will go on to listening to your equipment and what the tubes are doing instead of listening to music.
You will accumulate a large collection of tubes that’s worth half of what you spent on them initially. With today’s prices on vacuum tubes having 3-4 complete sets of tubes for VAC Avatar SE is about $3,000 - $4,000 for the modest non NOS  nothing fancy tubes. Before you know it, you will be thinking that spending this much to upgrade my table or cartridge or get an awesome phono stage would make so much more sense…but you’re stuck with tubes, looking at bias meters and scratching your head trying to figure out which tubes are contributing to the issue you’re troubleshooting. That’s a ton of fun and man does that add to the overall enjoyment of the hobby! 

Re room acoustics, agree with speaker systems, but don't forget headphone and nearfield systems. The most dramatic change for me was with a Woo WA2SE headphone amp going from stock to WE422. A clear quality improvement. Also rolled the AU7-style tubes on the WA2, but much less of a difference; more flavor than quality.

I am not a pathological roller. Did a bit of experimentation early on (5-6 years ago) since then have not bothered re-checking. Rather enjoy the music.

+10 on the room priority but sometimes that isn't easy, or quick. So assuming you have decent cables, tubes can make a big difference especially in source components. But, I'm referring to going from low-cost, new tubes often supplied with new gear, to well chosen NOS (in my experience).   

More transparent cables will reveal input or output tube changes even more so than veiled over cables. The same in reverse with more transparent tubes vs. more veiled over tubes when comparing - both matter.  

As an experiment I recently custom ordered a lower cost $95 mainstream Mogami W2534 Quad RCA cable pair with Neutrik and Amphenol connector ends. 

• With these cables, reportedly "neutral", and nothing exceptional about the design, decent copper used and decent connector ends used. To begin with I’m not hearing extra texture or tone with tube changes.  So, if its "not there" to begin with, it’s questionable. 
• With my higher end Cardas interconnect cables, any tube changes, input or output, I simply hear a differences in changes, more.   

In summary, I’ve concluded more than 20+ times over decades that better cables and more transparent tubes allow you to hear other changes upstream or downstream even more. With that said, fine tune tone, texture, and soundstage from there on both sides +/-, in small increments is one way to approach it. 

Back to the old "everything matters" reference. There is an interdependency with both, imo. 

Speaker positioning