I think you mentioned that you purchased sterile seed starter mix. This is my first year attempting to grow seeds in the house for transplanting later, but I have been reading lots of articles and watching a number of YouTube videos on the need to sterilize any and all seed starting and potting soil mixes to kill fungus gnat eggs.
The 3 methods I have seen are cooking the soil in the oven, microwaving the medium, or dumping boiling hot water over the soil. Most of the people I have seen on YouTube use the boiling water method, which is what I plan on doing with my starter medium. I have my seed starter shelf in our second bathroom, so the last thing I want is fungus gnats flying around in the house.