Square Carpet tiles (sometimes called carpet squares) should be laid on a flat, sound, level surface. There is no need for underlay but, if required, something fairly firm with very little give should be used, such as cork.
A soft underlay will allow the tile corners to pop up if you depress the centre of the carpet square, and this should be avoided. For noise or heat loss issues, it is best to insulate the floor with an insulation board first and lay your tiles directly on top.