Recently (yesterday, actually) I ask a question about writing an AI character. The question get a fair amount of attention and there were several first time posters. They popped up in the First Post Review Queue, but I felt that it would be awkward for me to say something like "Welcome to Writing.SE thanks for the answer to my question. See the help center, etc. etc." when I am technically asking for their help. Therefore I didn't do it. Was I right in this assumption that this would be wrong (or at least odd)?
It's absolutely okay to greet new users under your own posts - please continute doing this!
In general there are no guidelines about greeting new people. It's just a nice thing to do so that they know where to find the most important resources, such as the tour or help center. That means it's totally fine to greet them when they pop up under your question.
Your question probably was in the Hot Network Questions and received a lot of traffic from other sites, which is why there were so many new users. Welcoming them is a very good thing and I would like to encourage you to continue doing this! Good job!
For more information see my answer over on WorldBuilding.SE to the question:
I agree with this answer -- definitely ok!
One general suggestion, though (not aimed at anybody in particular). We've gotten occasional flags on welcome comments that are more "direct"; if you say something like "welcome; please read our help", it can come across as "you did something wrong" even though that's not what you meant. I try to phrase these comments along the lines of "welcome! thanks for this interesting answer.1 You might want to check out our short [tour]". Or, for a post that needs some work, something more like "Welcome! We're a little different than other sites; we focus on Q&A more than discussion. Please check out our short [tour] for more about how the site works. I hope to see you around."
These are off-the-cuff examples; please don't take them as holy writ. :-) The key point I'm trying to make is that I try to read my comment through the new user's eyes and mitigate any unintended chastisement.
1 If it is, of course.