Personally, I think washing new pillow ticking is best done by hand in a kitchen sink full of warm water.
All you'r needing to do is to wash out the "sizing" that was applied to the material. Sizing is basically a starch which is soluble in water. It is used to keep the material smooth so it is easy to cut out with patterns and scissors or machine cutters which the big clothing companies use.
A bit of detergent in the water on the first wash, some elbow grease, then drain the sink using a mesh basket in the drain.
Pick out all of the loose threads in the drain basket that came off of the material during the washing.
Then, refill the sink with warm water and apply some more elbow grease to rinse the soap and remaining sizing out of the cloth followed by draining the sink again, using the mesh basket to catch the loose threads.
My reason for going this more difficult way is, there will be a lot of loose threads that come off of the cut edges of the cloth. Many washing machines don't have filters on them to catch these loose threads and letting the machine send them down your drain is an excellent way to plug up your plumbing.