Large files don't export properly

I am completely new to PS and want to understand a bit of strange behavior.  I got PS for final editing of very large, stacked and stretched astrophotography images.  I output them from an AP processing program as 16 bit tif and then open in PS.  My current image is 127 x 48 inches at 72 pixels per inch.  After a number of levels and curves adjustments I get it where I want it with crisp blacks and good color.  But, if I try to export a png or jpg, flatten the layers, just about anything, the output is noticeably tinted magenta. 

If I resize the image to from 5% to 20% smaller, the tint becomes progressively less evident.  If I resize about 25% or more, the tint effect disapears.  

I want to understand why I am experienceing the proble so I can avoid it in the future.  Should I simply rescale the images before editing in PS?   How far down would it be resoanable to scale them without losing details for viewng online?  How about for printing?  If I just need to read the Fing manual, feel free to tell me so.