In the video I've attached, it clearly shows that I get the invader kill and all of my team is still alive. Per the text of the quest, I have denied the invader from killing any of my teammates. Though I did not do it within the first 10 seconds of their invasion, the quest does NOT specify that as a requirement. Yet, the quest step for me to perform an invader kill on an enemy before they kill any of my teammates is still incomplete. Bungie, this is either a bug OR the quest neglects to give all the proper information on the quest step. I am requesting that you either update the text of the quest to match the ACTUAL requirements or give me my credit for doing what was specified in the quest. It's very frustrating trying to complete something with only some of the information.
The quest step does require you to get the invader kill within 10 seconds of them invading and before they defeat any teammates. The official note from Bungie regrading this was linked by TuxyDoh. I'd like to add some aspects that have not been mentioned in this thread. Destiny has always been about discovery, so not everything will be explained in full detail in-game. It's for us to figure out what a specific challenge needs. It would, at least in my opinion, diminish the experience if we were handed everything on a silver platter with little left to discover. These mysteries and challenges are what makes the game great, as well the community coming together to figure out the next secret. Also, it's not always possible to cram in every detail into the descriptions, as the space for them is limited. This is not to say, that there aren't any triumphs or quest steps that could use some revising, but I don't believe the ones that already have a known external addition can be counted into this category. Another thing to note, is that any issue marked for investigation by Bungie, will need to get prioritized based on impact to users. If there already is a known workaround, the priority naturally decreases and more vital issues get prioritized over it. So, if you choose not to complete the step until the description is updated, that is totally up to you. I do understand that some don't feel like it should be necessary to look for answers outside of the game, that everything should be explained in the game. However, as already mentioned, this has always been the case with Destiny; certain things are left for us to discover.