So I just set up a game and experimented with this a bit.
As has always been the case, the reliever appears to need two things to get the first-batter upgrade:
He must have a reliever * asterisk on his pitching grade (pitchers rated as starters-only don’t get upgraded).
He must face a batter hitting from the same side (ie. lefty-on-lefty or righty-on-righty).
But you probably already knew that.
Also… the upgrade does NOT appear to happen if the half-inning hasn’t begun yet. I tried making a change between innings. All the criteria was there, but the reliever did not get an upgrade for the first batter of the inning.
But as long as the half-inning has started (ie. a batter has reached base or made an out), the upgrade now appears to work EVEN IF there are none out. I believe that may be different from in the past. The GO Support people may have recently tweaked the game engine on that.