I do not believe the above text is current and that non-status companions on separate reservations can now be added to both F and C+ upgrade lists as long as they are on revenue (non BE) tickets (although, as noted above, they may need to be on the same itinerary). Also, while DL has added the ability for non-status companions on award/PWM/Companion certs on the same res to be upgrade eligible (at Medallion's status level), it seems that those companions are still ineligible for upgrades when booked via those means on a separate reservation (although companion certs already require you be on the same res). Unfortunately, it looks like DL neglected to update the above text block to reflect the recent changes. Also, there's no benefit that I can see in adding someone with status on separate reservation as a companion since they are upgraded separately at their own window anyway (unless I'm missing something).
Note the following text in the News release from April 6th and the "same reservation" requirement --
"Now traveling with your companion is even better. Starting April 6, 2017, companions traveling with Medallion Members will be eligible for Complimentary Upgrades not only on paid tickets but Award Tickets, Miles + Cash tickets, and Pay with Miles tickets. Companions traveling with a Delta SkyMiles Credit Card Member on a SkyMiles Companion Certificate will also be eligible for Complimentary Upgrades.
Here’s what Medallion Members need to know:
A Medallion Member and a traveling companion may both enjoy a Complimentary Upgrade to First Class, Business Class or Delta Comfort+® when traveling on Delta and Delta Connection carriers, as long as that companion is a General SkyMiles Member or a Medallion Member in the same reservation."
In the OP's case, there must be different reservations because the OP and companion are flying different routes. The question is about upgrading the companion on only the segment that the two routings have in common.