I don't have a Turbo so I don't know what the exact settings on the Recent Calls page are, but if you are in the dialer and looking at recent calls there should be a menu control bottom right. I know that on the Droid Maxx you can show Incoming only, outgoing only, or missed calls only, but I've never seen a setting that shows outgoing and missed calls only.
Does your company phone have an Exchange account set up? I wonder if there is some weird Exchange policy that prevents storing incoming call logs?
I have an app called SMSBackup+. It's main function is to back up SMS messages sent and received to a GMail account, but one of the options it has is to back up call logs, too, to either (or both) a GMail account or Google calendar. If you can find no other solution and there is a way to install that app, you can use it to back up your call logs and see if it stores your incoming calls, too. That may be a slightly awkward work-around.