Trip switch goes off 50% of the time when turning off an appliance
Really hard to answer this because there are unknowns. 


What does that earth light mean? No earth/ground/ or there is a ground.
How's it wired inside? If they wire it between live/hot and earth/ground that is already an imbalance. Maybe the switch on the 6-way is double pole and neutral opens before the hot. That will cause an imbalance and may trip it. 


Try another 6-way with no earth indicator.

Or unplug the strip not switching off the strip's switch. Just leave it on.