first congrats on rescuing and getting it to rebloom. Aerial roots are common on many orchids but very common with Phals. In nature, Phals don't grow in a medium but on the surface of trees, with it's roots exposed to a moist atmosphere.
When I grew Phals in my home, I would mist the aerial roots. I do believe some of yours are due to the position that the plant is growing but it is a rare Phal that doesn't grow aerial roots.