If you raise the vehicle & turn the steering wheel without the engine turning over, you may have the pump reservoir spill over.
Idling the engine allows the pump to circulate the aerated fluid back to the reservoir so the bubbles can pop.
If the fluid is Badly aerated, such that it looks like a pink milkshake, without applying a vacuum to the reservoir cap while the engine idles, it might take several cycles of idling the engine & turning the steering wheel lock to lock to bump the stops, to chase most all entrapped air back to the reservoir, stopping the engine so the bubbles have time to pop.
The aftermarket additive you used may deter the bubbles from popping, so the deair cycle may take longer.
Adding a slight vacuum through the reservoir cap vent hole, can hasten the deair cycle, by causing the bubbles to pop quicker & having the vacuum applied while the engine idles & you turn the steering wheel lock to lock to bump the stops, while the p/s pump circulates the aerated fluid back to the reservoir, Really cuts the deair time.
If you want to change the p/s fluid by using the turkey baster method to remove the fluid a little at a time, its better that not changing fluid at all, but a system flush with the P/S pump return line disconnected at the cooler, while a friend cranks the engine with the starter, is more complete, as it removes most all of the old oxidized fluid & debris its carring, from the pump, rack, cooler & lines, so it won't recirculate & mix with & contaminate the new fluid, weaken its ad pack & hasten the new fluids demise.
SO, if you want to Completely flush your power steering system of old fluid, while adding new, maybe consider having a friend help you do this routine Power Steering Fluid Filter
It includes adding, or changing the P/S inline filter after the flush service, which you may or may not wish to do, but all of which you can do for Way less than $54!!!!
More thoughts for consideration, let us know how it goes.