With the ICAO and other enroute charts, what you see on the map is literally the same thing that's on the paper. There isn't a way to change that. However, if you turn off the ICAO / enroute layer, the digital version of the map will still be drawn from the PocketFMS digital data, just like it always was, so those other airports would still be there. Airports from the digital database aren't drawn on top of the airports on the chart because in many cases they'd obscure the other information on the 'paper' chart.
If you've added any user waypoints (which aren't airports, per se), they'll show up on top of the ICAO/enroute charts layers though.