Tergosternal muscles help in the blood circulation in a cockroach as well as in movement of the wings for flying. I came across a question that claims that these muscles are used in blood circulation as well. I can't seem to see a relation between blood circulation and these muscles.
It is not the tergo sternal muscles that are involved in blood circulation in cockroaches. Tergo sternal muscles help in breathing. It is the Alary muscles that help in blood circulation. The alary muscles are associated with all the thireen chambers of cockroach's heart on either side of it. The alternate contraction and relaxation of these muscles help to pump the blood.
Sources which support my answer: