The filter isn’t oily. Also not a genuine one is oily filter. The auto parts shop rep told me the genuine air filter costs 3600/-, while the local one is 600/- and he said both work fine, so I opted for the local one.
However, I’ve noticed that the underside of the air filter is already getting dirty, and the car hasn’t even run 500–600 km since the air filter and spark plugs were replaced.