Got a bounty, recovered the ship, and that's how it was.
Now, I haven't tested it in an actual fight and didn't pay too much attention when I was fighting it, but if both cores stack it would be pretty ridiculous.
Not using any mods that alter vanilla variants or create new ones.
Edit: Just making sure it's clear: With the Advanced Targeting Core, it's impossible to install either DTC or ITU, but this Paragon had it installed for some reason. If I remove it, I can't install it back so it's working as intended, but I can easily keep it and make use of what appears to be a bug.