White holes are described by the time reversed Schwarzschild metric. A test particle which is gravitationally attracted to the black hole's event horizon in the Schwarzschild metric is also gravitationally attracted to the white hole's event horizon in time reversed Schwarzchild metric.
Still, white holes are described as a region of "outward-flowing space time".
How are both compatible?
There is no contradiction. “Attractive gravity” is about acceleration, which is directed toward the massive body. While “inward-flowing spacetime” in the river model of black hole (or “outward-flowing spacetime” for a white hole) is about the direction of velocity.
Under time reversal velocities reverse direction, while accelerations stay the same. If you play a movie depicting an object falling toward Earth backwards, you will see an object “jumping” upwards, but acceleration would still be directed downwards.
And it is best to always remember that how “space flows” is dependent on how one decomposes spacetime into “space” and “time” and this can be done in many ways, so one such representation does not preclude another from being equally true.
