Try this - just activate an instance of the Tape Sim in the ProChannel for any softsynth (I am using simple instrument tracks if it matters). Turn it on and set "noise" to about 50%, and confirm it is working correctly by playing something from the synth. (I have tried both Lounge Lizard full version and Truepianos full version). Turn down your master fader...... and wait. (Somewhere around 45 minutes to an hour, not really sure on the timeframe.)
I have the 90db meters (default I think) on track view - and I can watch the sound slowly climb up on the meter - turn off the Tape Sim and its gone, turn it back on, and the meter continues to climb - 
Last night I left my DAW running with everything as I left it with an instance of the tape sim in Lounge Lizard - later that evening I heard a deep thrumming sound from my studio that was evidently originating from the Tape Sim - I reset the sound card, no difference - turned off the Tape Sim, then back on - still there. I can remove it and put in a new instance, and it is gone. This morning I confirmed the issue by using a different soft synth (True Pianos). 
Can anybody else confirm?
 
 

Me too.

gswitz
Me too.

Thanks Geoff

It looks like the "noise" control determines how quickly the sound rises - if you turn it to 100%, and you have 90db meters, you should start to see the meter begin to climb within a couple of minutes or so. If you turn the "noise" control to 0%, the meter climbs more slowly, but it still occurs.
Definitely needs a fix. 

We are looking into this issue.

has happened here too. twice.
 
Walked away from my computer for a while and came back to the loud humming. Weirdly enough I knew who the culprit was straight away.
 
 
 
edit: ill add mine was inserted on a bus.

Andrew Rossa [Cakewalk]
We are looking into this issue.

Thanks Andrew

perfectprint
has happened here too. twice.
 
Walked away from my computer for a while and came back to the loud humming. Weirdly enough I knew who the culprit was straight away.

Thanks for confirming

Attempting to Repro now...

FWIW, I was able to reproduce this, and the "loud humming" is a 60Hz hum that Tape Emulator adds in addition to the high-frequency "hiss"; it's actually the highest amplitude part of the noise signal. This is the first plug-in I've seen that deliberately emulates a ground loop. I can't help but think this emulator is one big April Fools joke.