Caulk on top of grout in tiled shower
Grout will also mildew over time. The other problem is that grout is not as good as caulk in repelling water which is the reason it is used where shower surfaces meet at 90 degree angles. Your installer did the right thing by caulking those corners.
Eventually, you'll want to remove the old caulk as it starts to break down and recaulk it. It's a basic maintenance process that's necessary in keeping any shower leak free.
Additionally, new grout should be sealed which will help maintain it.