Thank you for your post.
FAT and linear phase response are totally different things.
As you can see FAT is available in PSP MasterQ2, Neon, MasterComp and VintageWarmer. FAT is an internal double sampling and allows filters and other algorithms to work in a virtual analog domain to prevent from high frequency response distortion and excess aliasing.
PSP MasterQ2 with FAT engaged can process and sound similarly to analog equalisers.
Linear phase filters are something totally absent in analog. To provide their linear phase response they have to provide a kind of “pre ringing” as the response of the linear filter is symmetrical. Hence the more accurate linear phase filters are the larger latency of the algorithm is.
I hope that it will help to better understand major difference between filters used in PSP MasterQ2 and linear phase equalisers such as Neon HR.