Do not use any other optic that isn't zeroed to 100m or 200m.
Recommended long(er) range optics are [^] , [^] and [^]
If you use default CSAT recon pathfinder class, you can see that ASP is fitted with Nighstalker by default and the zeroing works.
Ultimately DMS is the best option. It even has russian style chevrons for easier bullet drop compensation. :)
Long story short, you just don't slap any optic to this weapon just like SMG:s
Everything here is working as intended. ASP just isn't a long range rifle as is stated by developers "We wanted something special with extreme hits, a low range, and built-in silencer".
So the problem is you are using wrong optics, it's the same thing for SMG:s, any optic that can't be zeroed to 100m or at least 200m, will not work for them.
EDIT: SOS sight (the name has changed) is now set to minimum of 300m so it doesn't fit ASP anymore.