The reserve tag of that unit only determines their supply and reinforcement prioritiy, nothing else. They use the same template as an elite unit of the same type, the elite unit simply gets better equipment earlier. You can probably just click on the reserve division and raise their priority.
As far as I understand, there's no such thing as tags for a division, but instead for the whole template. Correct me if I'm wrong.
There's another issue related, besides quality of equipment. Said reserve division (with a reserve template) saw a lot of combat unexpectedly and now I want it to perform first line duty. However, for that role it lacks armor/arty/whatever. Now I want to upgrade or switch the composition of it's regiments, but whitout changing the whole "reserve" template.
In order to do so, I think a "switch template for the division" button is needed.