Howdy.
Good bass playing, good tone on the demo. Your P w/ flats will get you 60% of the way there. But the rubbery, strong attack/quick decay, strong midrange, and short-scale/hollow body-specific harmonics will only come with...well, a hollow body. Even more so if it's short to medium scale. That's the stuff he's after, I'm guessing.
Generally speaking, that breed of bass actually speaks more...it's less transparent, wide and pillowy...it tends to be more focused, pointy, and again: midrange-oriented. A decent example is me playing my 90's Guild Starfire with some very average D'Addario Chromes on it through a 90's B-15R on the Beck song "Paper Tiger". It's recorded with a 47 Fet and some dirty compression and the amp driven a bit. That combination of factors give it lots of personality, and of all all the factors, the biggest contributing factor is the bass.
At this point, you should simply ask him for some specific references. Any good producer is obliged to provide those if they are making general comments...it's the support for the argument that's essential for mutual understanding and moving forward.
Good luck,
Justin