Tebbe's reagent itself does not react with carbonyl compounds, but must first be treated with a mild Lewis base, such as pyridine, which generates the active Schrock carbene.
Also analogous to the Wittig reagent, the reactivity appears to be driven by the high oxophilicity of Ti(IV). The Schrock carbene (1) reacts with carbonyl compounds (2) to give a postulated oxatitanacyclobutane intermediate (3).  This cyclic intermediate has never been directly isolated, presumably because it breaks down immediately to the produce the desired alkene (5).