To my knowledge:

Anyone who has been vaccinated against HepaB, can test positive on some routine test. e.i. (HBs test) Hepa-B surface antibody test.

But this is a test to determine your level of immunity against Hepa-B, a positive result indicates your immunity to hepatitis B from the vaccination or a recovery from an infection. But NOT to be identified as a risk here.

Through the used of more sensitive and sophisticated lab test, it is possible to differentiate between a Hepa-B Antibodies produced by the disease or been exposed by any means AND a Hepa-B Antibodies produced by the vaccines.

It is also best advisable though not necessary for us to carry our Hepa-B vaccination card/evidence especially for a medical employee like us.