Do you think it is a issue with it being a tube pre. Would a solid state pre have the same problem?
No, and yes.
Hum is a simple subject that only seems complex because of all the many different situations it crops up in. But hum is as simple as this: Any time you have different paths to ground you risk getting hum.
Your hum happens because in one room you have the turntable plugged into one path to ground, which presumably the ground goes to the phono stage, which is connected to ground via the outlet they both are plugged into. But then its connected via RCA to another path to ground, the amp in the other room, which has its own path to ground. Your extension cord eliminated the hum because then everything had just the one path to ground.
This one simple rule comes in real handy. Like you would never run multiple dedicated lines you would run one. What you have done is, in a sense, build a system with multiple dedicated lines. Only they aren't dedicated. Just different.