Light aircraft pilot reported an NMAC on approach to TKI airport when a faster twin turboprop aircraft; who was reportedly not in contact with the Tower; overflew him.

Narrative

Aircraft (A) established contact with McKinney Tower with information; approximately 6 miles north of JIPUK. Tower updated altimeter setting. Pilot (A.1) was conducting simulated instrument flight at 90 to 100 kts. at about 1;900 ft. MSL and descending. Pilot (A.2) was Safety Pilot. (A) was on a long final for landing at McKinney Runway 18. McKinney Tower warned of a fast approaching [turboprop aircraft] from behind and that they were not talking to that aircraft. Onboard traffic system confirmed rapidly approaching aircraft. Pilot (A.2) was looking behind to try to see him. Tower gave instructions to (A) to turn right a number of degrees; which (A) complied. When traffic system showed approaching aircraft to be about to breech one mile distance; Pilot (A.1) ended simulated instrument and began looking behind for traffic. The collision alert warning went off; and almost immediately; aircraft (B) appeared from over the tail on the left side; only a few hundred feet distance. It is believed that (B) violated 91.111(a); 91.113(f) and 91.113(g) and thereby created a collision hazard.After (B) passed (A); Tower cleared (A) for number two landing.* Aircraft (A) then encountered (B)'s wake vortex and rolled approximately 45 degrees to right; with immediate recovery by Pilots (A.1) and (A.2). The remaining flight was nominal. *There is no issue or complaint with McKinney Tower clearing (A) as Number 2; as that did not create an unsafe situation.The safety problem is that (B) did not take evasive maneuvers to give the legal right of way to (A). Aircraft (B) was overtaking (A) and was at a higher altitude.It is unknown whether (B) had been talking to Regional Approach. If so; Regional should have informed him of traffic and provided vectors or altitude restrictions to avoid a hazardous condition. 'Traffic in sight' does not relieve a pilot of minimum safe separation distance.Improvement: Pilots of (B) need to be reminded of right of way rules and to maintain minimum safe distance; and that may require veering off a localizer in VMC.Improvement: Although in conflict with Tower heading instructions; (A) could have conducted a significant yaw in order to see directly behind it; thereby realizing it needed to make a hard west turn and dive to get out of the way of (B); which was disregarding safe separation.