I'm not sure, what you mean by "flowing up", but I'm assuming you mean "flowing poleward". At any rate, the Coriolis force is completely independent of the pressure field - it is a purely kinematic law. The pressure difference only drives the poleward movement, which is, in turn, deflected by the Coriolis Force.

To illustrate, imagine you are standing on the north pole and you throw a ball south (really hard). The ball will fly straight south whereas the earth beneath it is rotating eastward (to the left from the north pole perspective). This means, from the earths perspective, the ball is bending to the right.

Similarly, If you're standing on the equator and you throw a ball northward, it has a higher eastward velocity compared to the earth's surface more northward. This means, from the ball's perspective, the earth is rotating westward, or, to the left and from the earth's perspective, the ball is, again, deflected to the right.