When you upgrade a turret in the Defense Lab, you are essentially unlocking that level of turret. 
This won't change the level of any existing turrets you have placed, however. You still have to equip your defense platforms with the turret you've upgraded.
So for instance, if you had a level 1 Hellfire on a defense platform and then upgraded to level 3 Hellfire in the Defense Lab, you'll still have to replace the lower level Hellfires on your platforms with the new upgraded version. 