I have a lv 50 soldier with both the shield and Gemini. You deploy 2 turrets and each one gets a shield. Each shield can take a set amount of damage (about one hit from this game's version of crawmerax, sometimes 2 hits; assuming you are lv 50) and if one turret's shield goes down the other can still remain up until the turret is recalled or it's timer runs out or that shield takes sufficent damage. I cannot swear to it but i BELIEVE, based only on my experience playing the soldier, that the capacity of the phalanx shield is based on your level. at lv 50 it seems to have about 45k. that may seem like a lot at lower levels but at 50 it burns up pretty quick.
After playing a new soldier from 1 to 45 without any power-leveling and getting to test the Phalanx Shield over about 20 levels I would say that the capacity of the shield is absolutely linked to your level. The shield capacity of your turret's Phalanx Shield appears to be about equal to a good capacity Pangolin (turtle shield that offers high capacity while lowering your overall health) that you could use at your current level.
I also tested the average time the turret would survive after the shield went down and then did a skill reset and tested to see if adding the shield might have a drawback like lowering your turret's health. I saw no noticeable difference in the health of my turret with the shield VS without, but obviously it's overall survivability was much better with the shield to absorb damage before the turret itself could be hit.
I changed the shield I was wearing several times and saw no difference in the performance of the Phalanx Shield so it does not seem to be linked to your players equipt shield in any way.