Instructor pilot reported a NMAC while in the traffic pattern at a towered airport. The offending twin engine aircraft was practicing an engine out approach and drifted off course. The twin passed overhead of the instructor's aircraft.

Narrative

My student and I were on an extended upwind of Runway XX; and entered the left crosswind per tower's instructions. I observed on our TAWS system that a company Seminole had drifted off of the extended centerline by approximately one or so miles into our crosswind leg. The display indicated a vertical separation of them being approximately 200 feet above us and I would estimate 1/8 mile separation. Both my student and I only noticed the Seminole after seeing it on TAWS. We did not take any immediate corrective action as we were stable at pattern altitude; and crossing in front of and below them. Tower instructed the Seminole to turn right immediately; as they were supposed to enter right traffic to begin with. Tower later had us call them to discuss the situation to which they advised that the Seminole had been conducting a simulated engine out; which resulted in their leaving the extended centerline.After a phone call with Tower; it appears that a simulated engine out caused Aircraft Y to drift into the left crosswind of Runway XX; where my student and I were. The TAWS indicated a vertical separation of approximately 200 feet; and I estimated a lateral separation of 1/8 of a mile or less. No evasive action was taken as the Seminole passed over us. After we had visual contact with the Seminole; I heard the Pilot flying of Aircraft Y say; 'There's a plane right there.' Tower instructed them to turn right immediately; advising them that they had drifted off of the Runway XX upwind. During a discussion with tower; they informed me that the current smoke and haze is making it difficult for them to assist us with see-and-avoid so that may also be an on-going safety hazard.