They did not use two transformers.
T1 is not a transformer it is a "common mode choke", which is intended to prevent the high frequency noise which is generated by the switching supply, from being conducted back into the mains wiring.
before you blow your hat off, follow the datasheet very carefully. C1/C2/C3 need to be rated to at least 400V. I would not suggest making this circuit on veroboard either