Do these machines solder the component? Or is it then necessary to put the PCBs in the oven? thnks!
Put solder on the pads. This can be done with a solder mask - a thin sheet of metal with holes cut where the pads are. Solder paste is scraped over it and then the mask is lifted off, leaving solder on the pads.
Place components. This can be done manually or with the pick and place machines described here. The solder paste is sticky so there is something to hold the components in place once placed.
Reflow. This is done by putting the now populated board into a special oven. This oven will put the board through a particular temperature curve ('profile') which melts the solder then lets it cool. The surface tension of the solder on the pads helps here - it pulls components that are a fraction off into perfect position (assuming the pick and place got it close enough and that solder is on pads where it is meant to be).
What you’re referring to in the first paragraph is just called a stencil.
You put the PCB in a reflow oven afterwards.