they take on the texture of whatever block they are placed on.
so place a wall tile where you want the modified thing to be, then place the modifier on that wall tile. it will turn that square block (wall) tile into whatever your custom modifier is
you can do some nifty things with modifiers by using multiple modifiers next to each other modifying different walls. for instance, make a table modifier and place it on a wood wall texture. now make a new modifier that is a small cylinder, and offset the modifier to left 64 units. put that modifier on a wall texture that is directly to the right of the table, and you can make a coffee cup that sits on the table.