The containers need no more water until the seed germinates. Under no circumstances should plastic covered containers be placed in direct sunlight. Once seedlings are growing, remove the plastic and provide proper growing conditions. Give the seedlings adequate light. Even the sunniest windowsill provides varying amounts of light and only from one direction.
Windowsills often lack adequate humidity and are too warm for best seedling growth.
Cool white fluorescent lights placed three to six inches above the seedlings are a good light source. The length of time the lights are on varies with the type of annual grown. Some general guidelines are given here, but read the seed packet for additional information. A time clock will make sure the daylengths are regular. If only one light fixture and time clock are used, the plants must have compatible growth requirements.