What will be the major product of the reaction between (2R,3R)-2,3-dimethyloxirane and triphenylphosphine?
First, note that with the mechanism you have drawn you should expect to get a mixture of cis and trans isomers. In the intermediate you drew, rotation about the C–C bond will be fast and will lead to loss of any stereochemical information that was previously there.

The only way to get exclusively trans-2-butene is for the reaction to occur in a single step without a discrete intermediate:



However, that's not the case. The mechanism of epoxide deoxygenation by triphenylphosphine isn't a concerted pathway, but is stepwise.

Triphenylphosphine opens the epoxide ring first;  because this epoxide is symmetrical, it doesn't matter which carbon you attack. This gets you to a charge-separated intermediate 1a (a "betaine"). These species tend to combine their positive and negative charges if they can, and here they certainly can, but first the C–C bond in the middle has to rotate to get the negatively charged oxygen and the positively charged phosphorus on the same side (1b). Note that this bond rotation brings the right-hand side methyl group to the front of the molecule.

Cyclisation to the oxaphosphetane 2 then occurs, and collapse of this to give triphenylphosphine oxide and cis-2-butene is concerted and stereospecific, exactly like the final step of a Wittig reaction.



See also the Barton–Kellogg reaction for a similar mechanism, just with sulfur instead of oxygen.