A light spray of dilute dish soap or insecticidal soap on the drip tray under a pot will render the water in such a saucer lethal to springtails, but that's only a small control on their population. It's a good trick to play on them the night before watering the plants. The soap kills the surface tension of the water, effectively wetting down the springtails' skin, and they drown.
They breed fastest when conditions are moist, and prefer soil wetter than peppers do. However, if you use organic fertilizers, they can feed on these (and the microbes that flourish in soil when some organic fertilizers are used), and their numbers can snowball rapidly. Even when soil conditions are fairly dry, they will crowd the moistest spots possible.
Once their population reaches a critical number, they turn to plant root hairs as a source of food, and your plants sicken quickly.
Diatomaceous earth will control them. Other -- more experienced -- gardeners may have other recommendations. When i have live cultures of soil-dwelling predatory mites (Hypoaspis miles), i establish populations in my seedling plants because springlails are so endemic on Coastal Vancouver Island that i suspect they get tracked into the house on shoes and trouser-cuffs every day. You may find that they never become a problem, depending on your water, fertilizer, soil mix, climate... and other factors (i'd guess). Light infestations of them are never a problem, in my experience.
