Mildew is a form of mold that develops if you have moisture, a source of food and the right temperature.  Since you aren't going to get rid of the moisture in shower, then you have to get rid of the food. You do need to ensure that there is good ventilation to prevent high humidity or the mildew will tend to occur as people in Florida and near the coast will testify to.

When you replaced the sealant at the bathtub transition to the wall you should have let it thoroughly dry out before applying the new sealant.  There is also a question whether there is a defect in the tile assembly that is allowing water to get to the back of the sealant that might be perpetuating this mildew issue?  The type of sealant you should be using is an ASTM C920 sealant, as required by industry standards, that is typically a pure silicone or urethane sealant.  You should have filled the void behind the transition joint with a closed-cell polyethylene foam backer rod material so there would be no void.  You then leave at least 1/4" depth for the sealant to fill.   I have found that clear silicone sealants that are mildew-resistant still can develop internal dark spots, so I now stay away from them and go with a colored sealant. Good luck.