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.
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While you raise a good point to discovery being a part of destiny, many users may have been frustrated by this quest when it first came out. The actual description of the quest is quite long. One of the longest I've seen, so rephrasing some of the text to simply read, "Acquire X medal in Gambit" would have given much better direction and less frustration as well as reduce the amount of text that the quest creator had to type. It would have been less work for them and less frustrating for the player. As it stands now, it's just a long list of words that when done by what is stated, does not produce the actual reward and only frustrates the player. That's been the whole point to my posts about this matter. I completed the text objective, but was told after the fact that you actually have to do this hidden objective because "we forgot" to put it in the details.
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While I sympathize with the description lacking in that respect, I'm not sure if I fully understand the determination behind the refusal to finish it, now that you do know what it requires, just because it's not written in the step. In any case, I wish you the best of luck on your journey.
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Its more that the frustration caused me to get angry, and I'm taking a break and breather from it. That's where the refusal to do it right now comes from. My frustration and anger at the lack of direct info from the quest to start having and having done the requirements in the text provided in the quest would only impact my game play performance, causing further frustration.