No way. While turtles are fairly primitive reptiles (with the exception of their ribs being outside their pectoral and pelvic girdles), they had already diverged from the line of reptiles that led to the ancestors of mammals very early in their evolution. Turtles are an evolutionary dead end.

No, turtles are probably anapsid reptiles, which have no temporal opening in the skull. Anapsid reptiles are among the earliest reptiles to evolve, but mammals evolved from therapis reptiles instead of evolving directly from anapsid reptiles. Therapsid reptiles in turn evolved from a synapsid reptile. Synapsid reptiles have one temporal opening in the skull and they also evolved quite early, but they almost certainly evolved from an anapsid reptile. Back then turtles have not evolved yet,. That means turtles evolved after synapsid reptiles did, and therefore synapsids could not have evolved from a turtle. Nevertheless turtles share with mammals the primitive condition of excreted urea as nitrogen waste. Most other reptiles and birds excrete uric acid instead.

Mammals therefore share an ancestor (an anapsid reptile) with turtles. That is true of virtually all other amniotes (mammals, reptiles and birds). Birds evolved from a diapsid reptile, and lizards, snakes, crocodilians and the extinct dinosaurs are all diapsid reptiles. Diapsid reptiles did not evolve from turtles, but their ancestor was almost certainly an anapsid reptile, since anapsids were the earliest reptiles to have evolved. I think you probably misunderstood what was said in the lecture.