I found the image below in an old book about vacuum tube rectifiers. Could someone explain why the negative terminal of the load is connected to the 6.3V transformer? I understand why it would be connected to the 350V transformer but not the other one too.
The 6.3V supply is for the tube heater. The heater and cathode get surrounded by a cloud of free electrons. By putting the heater at the most negative point in the circuit you ensure that these electrons are not attracted back to the heater.
According to the RCA Receiving Tube Manual (30th Edition):
As others have said, this would apply to other tubes in this device, not to the power supply rectifier.
Note the the heater-cathode voltage is rated at -500VDC to +100VDC (DC limitations shown in notes g, h). In this case, it will be running right at the negative voltage rating (-500VDC) since 350V RMS will produce about 500VDC, so the filament needs to be somewhere between the negative rail (call it ground) and +600V.
Also note that this is not two different transformers. As typical for the era, the plate and filament voltages come from two secondary windings on a single transformer. You can tell this by the fact the parallel lines (representing the magnetic laminations) span both secondary windings.