Let me quote the manual:
When you use a tripod, the Image Stabilizer should be turned off to save battery power.
The manuals of both lenses (1) (2) don't mention any automatical turn-off feature but contain the above instruction, meaning you have to manually take care of this.
As you see, there are no detrimental effects on the photos when keeping the IS turned on with those two modern lenses. It just helps you to save energy when you turn it off in scenarios when it's not needed. Personally, I always carry along backup batteries and don't worry too much about the IS's power consumption.
Generally speaking Canon's manuals are really good, trustworthy and cover a lot of details and you can download all of them as far as I know. I always recommend to have a look at the manual first.