So, do you and your primary have an agreed upon safe sex rule, and did your primary tell his new lover about this rule?
If you did, and he did, and homeboy still didn't wrap it up, then said new partner possibly has his own agenda and isn't interested in respecting the rules of the game.
If your primary didn't tell him, I would wonder if possibly he was uncomfortable about communicating clearly and honestly with a new partner.
Both of those scenarios would be pretty significant red flags to me; the first that this new lover doesn't really have your best interest and your primary's at heart, and the second, that your primary isn't really ready for poly and the super-clear communication that it takes. If you didn't have such a rule, might I suggest that you both make a very clear list of boundaries that you have in negotiating the poly swamplands. My newly-poly partner and my not-exactly-ok-with-it self just did this, and I feel a little safer for it.
I'd be pretty interested in the circumstances that led to this, if it were me.
At any rate, I support you in not having sex with him until everyone is
tested. STDs are a HUGE issue for me in negotiating my own relationship, and I understand how you must be feeling.