Well, there is no direct supporting evidence of Drilbur opening a shop in Paradice on either serebii or bulbapedia, the two sources that I know of. Yet, I found a sliver of hope on the shop: Salvage Treasure. A likely shop for Drilbur. (Source) Serebii explains that it is a mini game that enables you to get items like stones.
On the link you shared, I could read (thanks to Chrome) and make the judgement of that Drilbur will appear when you dig with a tool and offer to dig to find more tools at a price. Deeper Drilbur goes the more you have to pay. You can tell how far Drilbur can dig with the respective prices. The deeper you send Drilbur, the more likely you would find Pokemon tools.
I hope I helped.