Unfortunately, there seems to be some confusion. I need to take some/all of the blame, so don't feel bad.
The term "Voltage Regulation", can be confusing, as it seems to be used, for a number of things.
I was referring to Transformer "Voltage Regulation", which in very simplistic terms just means the voltage varies by say 10% (approx), as the output (load) current changes.
My concern was that it could make the transformer output voltage (AC) too high, for that PSU. Hence talking you into using a lower transformer rating (which you have), which solves that problem.
What you have just linked to, is another form of "Voltage Regulation", which is integrated circuit voltage regulator's "Voltage Regulation". Which also can vary with output (load) current changes.
Maybe a few percent or so, on a cheap/simple regulator (varies widely).
The idea is that the final voltage regulator (which is most of the PCB and circuit, you just bought), but can be just a simple 3 lead, integrated circuit regulator, just like you linked to. Will attempt to filter out (ignore), the transformers voltage variations, voltage ripple and things, to give a nice clean, well regulated output voltage.
BUT, it is not going to be perfect, and will also vary by a percentage (hopefully rather small), as the load (current) increases, temperature changes, and other things.