BE36TC flight instructor reported traffic on ADS-B was unknowingly conducting aerobatics resulted in taking evasive action and a NMAC.

Narrative

I was flying back from the practice area to ZZZ with my student. We decided to fly to the west of ZZZ1 to stay clear of the skydiving and student pilots. We noticed an airplane located roughly 6 miles from ZZZ1 on a bearing of about 335 but it showed up on ADS-B as being close to 2000 ft above us and we were laterally clear of it by about a mile so I judged that it would not be a factor to us if we stayed on our original heading. Since we were still close to the practice area; I was regularly reporting our position and intentions on the frequency.Suddenly; I lost visual contact with the airplane and I saw on ADS-B that it was descending rapidly and heading right at us. I immediately rolled the plane into a ~45 degree bank to the right and started descending to stay clear of the plane. Due to my evasive action; we got a TAWS warning. When I was sure that we were safely clear of the airplane; I started climbing again and started broadcasting on the practice area frequency asking whether the airplane we had to avoid was on frequency. When they did not respond; I switched over to ZZZ1 CTAF to try to get a hold of them and I asked them what they were doing. The pilot responded to me that they were doing aerobatics and that they had been on another air to air frequency. I informed him what the appropriate frequency for the area was but he did not seem receptive.I think the situation would have been avoided in several different ways. First; the other airplane should not have been doing aerobatics in that area because it was within 4 nm of a federal airway. Second; he should have done a better job of clearing the area before starting a maneuver. And third; he should have been on the appropriate frequency announcing his intentions because I would have stayed further away from him if I knew he was doing aerobatics.