I’m curious to know where you sourced your seeds. Very fresh seed harvested from fully ripe fruits or seed heads will germinate rapidly although 2 days is fast. My record for several species of chillis is 5 days. Bear in mind that that is the time taken for the seedling to break through the surface of the soil, so if you are germinating seeds on a damp tissue for example, you will see earlier germination.
Tropical plants do require some warmth, especially chillis and tomatoes. My outdoor beetroot and pak choi (in a coldframe) were up in about one week, carrots took much longer but they were sown in late February (early, I know, but they are outdoors in pots near a south facing wall, nothing ventured etc.).