I'm not sure we can conclude from his spell at Dortmund that Klopp prefers to buy cheapish, unpolished gems and watch them grow. Earlier in his Dortmund career, he probably wouldn't have been able to spend too much on individual players even if he'd wanted to, as the club was still recovering from nearly going bankrupt a few years earlier. With the rebuild he needed to do, it wouldn't have made sense for him to chuck major dosh on one or two star players as well.
In the seasons from 08/09 to 11/12, Dortmund assembled pieces of the puzzle with excellent value buys who eventually formed the core of the team which won their two league titles and a cup. Once that core was established, their next purchases in subsequent seasons tended to come at much higher cost. Reus joined from Monchengladbach on the back of a few successful seasons where he improved every season statistically in the goals scored and assists columns. When he joined Dortmund in 12/13, he was Dortmund's record buy at that time.
A season later, Mkhitaryan was bought for close to twice what Reus cost them, and Aubameyang joined at a couple of millions below Reus' price. Immobile, with a weaker track record, cost more than Reus, albeit there were a couple of seasons between their arrival. The numbers paid are probably peanuts compared to what Premier League clubs spend of course, but I think relative to the transfer fees paid by the Bundesliga clubs with the exception of Bayern and Wolfsburg, they're probably still on the high side.
I think with the core pieces assembled and with the successes achieved helping their financial standing (either directly in terms of sponsorships and winnings or indirectly through sales of some of their star players), Dortmund were now able to spend more on a small selection of individuals to replace departures.
So I'm not sure the evidence is strong enough to suggest that he doesn't flash the cash, or prefers to develop players rather than take players who've reached or are close to their full potential. The circumstances facing the club put them in that situation when they had to do that initially, and they were very successful with that, but I'm not sure that if Aubameyang right now tells Klopp he'd like to join us, he won't gleefully ask Ayre to sign a check for the 40m that Dortmund might ask for. Will be interesting to see how much of the current squad Klopp wants to retain, the number of guys he then deems we need to buy, etc. and then we'll see whether he spends 10m on five new guys, or 40m on a new chap and 10m spread over the other four.