Tube Phonostage Causing Rumble and Noises

@bpoletti is correct. Your turntable is sitting in a “hot spot”, a zone where bass frequencies are being amplified. If it’s near a corner, try moving it.

@agharion "I get the rumble when the turntable is not in use."

You've got me confused. Until now I thought the thread was completely about rumble while playing LPs.  Here's a line from your original post: "As soon as a signal was passed from the phono, the sub went crazy, it produced some subsonic noise that made the room shake. I then connected the phono to a tube integrated amp and I heard a loud distorted noise through my LS 3/5A."

So, I'm not sure where you go from here. You've got a ton of suggestions so guess you just keep experimenting. Have you brought in a different phono preamp to find if the issue is still present?

If moving the turntable and/or subwoofer does not work, your cheapest option, as others have pointed out is to install the KAB RF1 subsonic filter.  However, this will require that you insert the filter in between the phonostage and the amplifier and will require an extra set of RCA cables.  If you are using XLR connection from your phonostage to amplifier, then it becomes a little bit more cumbersome and will require xlr to rca converters (male and female). The RF1 filter can also be connected directly to the tape-loop if your preamp/phonostage has this option.

Other options include getting an isolation platform like HRS, SRA or Minus K depending on your budget.  And if all else fails, then get a phonostage with a built in subsonic filter. 

As an fyi, I had subsonic issues from my very first turntable, likely due to my suspended wood floors. In the initial stages, I did have to replace the driver on my REL subwoofer.  Subsonic rumble can lead to equipment failure over time if not mitigated properly.

@OP You indicate that there is no rumble when the Aexthetix phono stage is played via your Apogee. It's not impossible that the sub is reproducing frequencies that are below the bandwidth of the Apogees.

In terms of fault finding, you should borrow an alternative phono stage from your dealer - preferably solid state.

If that eliminates the problem then you know that the issue is interaction between the turntable/sub/phono stage.

Tubes are microphonic and the IO is relatively unusual in using tubes for all of its gain so the issue is, pardon the pun, amplified.

You need to use a subsonic filter. Many of us use them. They operate below human hearing and will solve your problem. @stereo5  was kind enough to offer you one to try. You should do it as your next step and potentially save yourself a lot of grief and expense. Springs won’t fix this.