I'm 5'5" and I have two road bikes and a TT bike, they all fit me well and I work with an excellent fitter.
My road bikes are 51 and 52 cm and my TT bike (which should be smaller) is a 48 cm. Given that you are 3 inches taller than me, I think there's a good chance the bike is too small.
If I had any questions about my fit, I'd go back to my fitter with my bike and express my concerns until I felt confident in my fit. My fitter has two free follow up sessions as part of the initial service and there is the option for paid follow up sessions as well. Maybe your guy doesn't have that, but I'm sure there's some mechanism for addressing issues like yours.
But he may just say to you: "I can't make this bike work for you, its too small" and if that's what he says, you either have to listen to him or find a different fitter.
As far as not knowing the term "inseam method," I am an 'expert' in my field and clients of mine will come in using jargon from their own reading. I may or may not be familiar with the jargon they using but my not knowing the jargon of people outside my field doesn't mean much.