There's 2 trains of thought generally for running in:
1. Take it steady and don't rev too high, etc.
2. Load the engine and allow it to rev up.
1. Is for "old" (poor tolerance) engines where there would be a lot of slop, so you would have to let it run gently to enable interferance parts to wear into each other nicely, making a good seal.
2. Is for "modern" (high tolerance) engines, where the manufacturing processes for the parts are much better controlled, therefore the parts fit together nicely as the tolerances are much smaller. Therefore there is less material to "wear in" to each other.
Running in oil is for number 1. I believe. I don't want to comment either way as I don't have enough engine building experience and don't want to advise you poorly. I'm not sure where 90's VW parts lie, I would imagine more towards higher tolerance, better parts (no.2) but that's just anectodal evidence! I know when I rebuilt my KTM 640 engine I was being told no.2, but that was manufactured in 2002 and low volume. A high volume product made circa 1991 may be a different story! I'd go by the advice of the person that built it, as they will be more experienced and you may find doing the opposite voids any form of warranty due to "abuse".
