The components are all soldered onto a small PCB module (the green one in this case), and then this module is soldered into a "cavity" PCB.
We made these custom pogo pin jigs and all they do is apply even pressure onto the module PCBs while they're in the oven so they solder reliably.
Making this PCB in PCB soldered process reliable was super tough. There were always cases of pads getting shorted or not soldered at all. The best way to diagnose was to just rip the modules off cold and look at the pads.
While there were a number of things to tune, the biggest improvement to the process was ordering new solder paste stencils with new diameters that compensated for the shorts or opens we were seeing.