Welcome to our forum.
"Should I take it I have done my due diligence here and, so long as I don't engage in any sexual behaviors with the 'Secondary,' not worry too much?"
I'll vote "Yes" on that one. I'd also suggest getting regular updates from your Secondary about how things are going with Newbie and if any changes need to be negotiated. Sometimes people's emotions change unpredictably and you need free-flowing communication channels between the four of you at all times.
Does Newbie know that you and your Primary are romantic/sexual partners? If she doesn't, she probably should know (lest she find out by surprise later on). I'd mention that to your Secondary, but ultimately the onus is on him to take care of that.
I don't foresee any big problems based on your story so far. Proceed with caution and you'll probably do well.