No. They were fully conscious of their position, in terms of economic power and monopoly. The Sherman Anti-trust Act was passed in 1890. They no doubt believed they had accumulated enough of the market to sustain dominance, while the overall pie continued to expand.

Rockefeller paid ransom sums for decades to buy out competitors (most of which were junk operators at best) to keep them from tanking the price of oil by dumping new strikes onto the market (a very frequent occurrence). His entire goal was oriented at market share + stability. The history of oil prices back then, was truly horrific, it was a constant boom and bust cycle that tortured most companies in the oil sector. Once Standard Oil accumulated enough of the market, including distribution (not as often talked about, they overwhelmingly controlled distribution), it could heavily control market pricing without having to own all the market. Their dominance in distribution is arguably the single most important thing they accomplished after the refining consolidation. With that gatekeeper status, they were able to demand other firms they didn't own adhere to their pricing levels, or have their distribution access cut off. In that way, they figured out how to stabilize the market pricing, without having to continue to own ~90% of the refining market.