I'm not sure what you mean by "song starters", but I'm guessing that you mean instruments like Dr. OctoRex, which has a run button to allow it to run "free form".
If that's the case, what you'll want to do is to unclick whatever button there is for enabling loop playback, and then add an pattern / loop lane to the sequencer track.
This will let you draw pattern / loop clips that switch between loop slots or patterns on the devices. To start/ stop sound at certain points, just place the clips where you need them.
Make sure to unclick that button, or the device will actually play as looped and from the sequencer, in effect playing 2 copies of the track with a slight delay.
A couple of tips about pattern clips... they have a black line at the end to show you when the pattern repeats. And on the Matrix, the clip length will vary with the resolution, so if you change it, you'll need to adjust clips.