Zip ties are a PITA to cut with knives.
If you watch the video clip in the OP, the emergency release is secured with a zip tie and they show that it can be easily broken if you have the grip strength to pull down on the release cord with some help from your bodyweight. So, for most folks, tools are not necessary if you need to pull the release in a hurry unless you're using some heavy duty zip tie.
It probably helps to have the zip tie oriented so that the release lever presses directly against the "buckle" part of the zip tie as you're pulling down on the cord. I can't be sure from watching the video, but I think you just need to break the tiny locking tab inside the buckle, rather than trying to snap the strap itself, to free the release lever. Using a knife, you're basically trying to cut through the strap, which is probably the strongest part of the zip tie.