GA Flight Instructor with student reported an NMAC while in the pattern of ACT airport requiring evasive action to avoid a possible collision.

Narrative

After departing for a training flight with a pre-solo private pilot student in the traffic pattern; we were advised to make left traffic for runway 01. Things started off strange when tower asked us to make an early left crosswind which we did at 300' AGL. Once established in the left downwind; we were advised to make a right 360. Upon completion of that; we were extended in the downwind. We were extended to the edge of the Class D airspace when tower asked us to turn left base. My student read back the call and then inquired to me off the radios if we should turn due to the aircraft. Due to my view in the right seat in a high-wing aircraft; I did not see what he was talking about. Within seconds; the multi-engine aircraft came extremely close to our aircraft crossing from our right to left. It seems as though they were attempting to join final for 01. Once the aircraft was in sight; I told tower on the radio that we were unable. We had to offset to the right about 20 degrees to avoid the traffic. After we continued on into the downwind having had to deviate due to the near miss; tower apologized and said that the traffic was supposed to be at 2000'. I am unsure as to why tower attempted to turn us onto base with that aircraft maneuvering inbound. Had we turned; we would have had a mid-air. My student is questioning the safety/credibility of the controllers at Waco tower. We understand it is a training facility but that was a negligent decision.