The Global Times warned that the U.S. would be "bound to pay the price" if it acts aggressively over Taiwan.
State media dismissed criticism after two Chinese fighter jets crossed the "middle line" between the mainland and Taiwan on Sunday.
Beijing and Washington vie for influence in the Asia-Pacific as China presses strategic regional goals.
Beijing faces a risk of a short-lived victory as "Trump will not want to be seen as having caved in.'
The successful intervention by Tillerson, suggests that in a White House-dominated administration, the new secretary of state could help drive decisions on some geopolitical issues.
The latest Chinese naval exercises have unnerved Beijing's neighbors, especially Taiwan which China claims as its own.
China has the capacity to hit back hard on both trade and security.
Beijing says the U.S.'s One China policy is the "bedrock" of the two countries' relationship.
The U.S. State Department said it had not been notified in advance of the ceremony and that it was inconsistent with U.S. policy.