It is not normal for a tube system to buzz. Some hiss is normal and maybe a bit of hum but buzzing is not.
Glad to see you have isolated the problem to the phono. Now the hunt is on. Try moving cables around to see if the buzz changes, try it without the turntable plugged into the phono stage to see if it is coming from the phono satge or the table, try grounding the turntable to the phono stage, try it without, try grounding the turntable to the preamp, try different interconnects, try moving the phono stage and turntable, try turning off other things in your house like dimmers and appliances.
You get the idea. There is no universal solution so you just have to keep trying things until you get rid of it.
When I first hooked up my latest phono stage the hum was as loud as the music. After trying umpteen different combinations of things you now have to stick your head in the horn to hear anything.
I am using a power regenerator for the high voltage supplies in my integrated and for my phono stage. It does make it a bit quieter but the main reason I use it is my integrated bias is sensitive to changes in line voltage. For your system it may not make any difference.