To my understanding, a true acoustic coupler would not have required a separate modem; you would have used either–or. Another way to think of this is to say that acoustic couplers generally would have had the modulating-demodulating hardware built-in. You needed an acoustic coupler if (and way back when) you were not allowed to directly electrically connect anything to the POTS landline network. You instead placed the landline phone handset onto the acoustic coupler.
~~ Intermission: A few minutes later ~~
Some googling (including of the Konexx) revealed that my memory is incomplete: As
this site puts it:
The acoustic coupler might also contain a modem, or the modem could be a separate device.
So apparently some simpler acoustic couplers did rely on a separate modem for the eponymous modulation/demodulation, and this also seems to be true for the Konexx. Since that's what you ordered, you probably did the right thing in also buying a modem too.
Things are not helped by the fact that some sources seemingly referred to acoustic couplers as modems, muddying the waters. Whether your acoustic coupler contained modulating/demodulating hardware or not, the main distinction would have been whether your kit was something you plugged into a phone socket in the wall, or whether it was some cradle-like thing you placed your or the company's telephone handset on.
NB: Softmodems/winmodems only became a thing later. I suppose they might work with a modem-less acoustic coupler. Maybe.
Rule of thumb: If your acoustic coupler has a serial port/cable that plugs into your PC, then it contains modem hardware. If it only has an RJ11 socket or phone lead, then it needs a separate modem. Apple's GeoPort
might have been an exception, but I don't even.