Yes you will get 12.5 mana back but once your mana drops below the cost of your spell's your left with only your normal mana regeneration.
In theory this doesn't matter because your last spell cast gave you 12.5 mana, meaning if you cast from 50 you'd start at 12.5 rather than 0. Tear theoretically makes it impossible to hit 0 mana, so the head start on your mana has a bigger effect than increased regen.
So while the refund will let you cast a handful of extra skills you will ultimately be hosed once the mana is gone.
Let me lay this one out for you. Jayce has 19.6 M/5 or 3.92 M/s at lv 18. His Shockblast costs 80 mana. On casting it he gets 20 mana back. In order for 25% mana regen to regenerate 20 extra mana at lv 18 you need to wait 20.4 seconds, without casting another Shockblast or any other spell. This is the best case for old Tear and new Tear is still better.
In a more realistic case Jayce isn't level 18, he's probably around lv 9 if mana's still a major problem. At this point he has 11.4 M/5 or 2.28 M/s. Under these conditions it would take Tear 35.1 seconds to regen 20 extra mana.
They play the long con and like to roam, use mana then recover it on the walk back. With this new tear they can't recover from an over use of mana like they normally would by just waiting it out and play safe.
They do recover mana, in fact they effectively recover more per second since they get a 25% bonus when they spend the mana they recover. You really seem to be underestimating this effect a lot. It not only slows your mana consumption but also increases the value of every piece of mana you regenerate by over 25%, the mana that you regenerate gets fed back into tear and when you spend that 20 mana you get another 5, then another 1, meaning that when you regen 80 mana you're effectively regening 106, a 26 mana swing.
This is the reason why I think every mage in the game will either go Tear>Cat or Tear>Lost after the changes, Tear works incredibly well with any form of regen, including just your natural regen.
buff jayces hammer e so he gets more mana per hammer hit.
This is a terrible idea. Remember that increased value per mana I was talking about? Well Jayces hammer swings now give an extra point of mana at rank 1 and an extra 5 at 5. Adding more mana into a positive feedback loop isn't a good idea.