My understanding is that the question can be whether the "one placenta" is two that fused together or one that was shared by both twins all along (because the egg split after the chorionic sac had begun to form, so there's only one chorion & placenta.) In the overwhelming majority of those cases, the egg splits BEFORE the amniotic sac begins forming, so each twin makes/gets its own sac and there's that membrane between them.
We had our first ultrasound right around 14 weeks (I wasn't sure of dates and the doc sent us to have the u/s to determine whether I was too late for the ultrascreen test, since we were going to have to drive almost 3 hours to get it if we wanted it.) We got more than we bargained for, because in addition to dating the pregnancy, they discovered the twin pregnancy then. At that point, they could not discern a membrane between the twins, so they sent me on to the bigger hospital to get a higher level ultrasound and a consult with the perinatologists there.
So, I had that second ultrasound within 3 days of learning about the twins. I was 14 weeks along, according to their estimates based on crown-rump measurements, etc.
They again saw one placenta and the second ultrasound revealed a membrane between them. So they were able to say that they were MZ/identical twins, and mono/di. The perinatologist said that it's possible it was a fused placenta, but that there were very clean edges and none of the characteristics they'd normally see in that situation, so he was comfortable saying that we were going to be expecting identical twins. He did say with an earlier ultrasound (maybe 6-7 weeks? I don't remember) they actually can count the layers of the membranes and determine with more authority what is going on with the placenta(s), but our twins' placenta showed every sign of being a single placenta from the beginning.
He did mention the increase of risks and defects....not an increase in risk for chromosomal issues, but other things. And he mentioned the issue of TTTS (babies were measuring one day apart at that point and I don't think he felt the need to raise any concerns, but he mentioned it as a matter of fact with mono/di twin gestations) and explained what they recommend in terms of increased monitoring a bit later in the pregnancy, to watch closely for any warning signs.
I'm not sure what the doctor was talking about with you. Maybe you got the wrong acronym, accidentally? Did you ask about Twin to Twin Transfusion Syndrome, specifically, or did you reference an acronym?
Maybe your peri was wanting to "protect" you from knowing whether you are expecting identical twins, thinking that you don't want to narrow down the gender even that much? (You'd know it is two boys or two girls, at that point.)
I'd say you could explain that you understand that you are carrying identical twins, that you don't wish to know their gender, but that you are wondering about what measures are in place for watching for/monitoring their TTTS risk. If they have reason to believe that the single placenta was two that grew together, they could put your mind to rest on that issue, and I'd guess that you'd be expecting either identical twins who are di/di (with a fused placenta) or fraternal twins, who always are di/di (with a fused placenta.)
I am new to the twin thing, but this is my understanding. And my guess at what the perinatologist was MAYBE talking about. Unless it was the ultrasound tech you were talking to, maybe, rather than an actual peri? Dunno!