In a contingent election the House elects the President and the Senate elects the Vice President. If the House is deadlocked then the Vice Presidential candidate elected in the Senate ascends to the Presidency. If the Senate is tied as well I'd assume the current VP gets the tie-breaking vote, but if not then the House Speaker would become President. The Senate elects the VP normally with each Senator getting 1 vote, but in the House it's done by state delegations instead of individual Representatives. This means that the 1 Wyoming Representative gets the same vote as the 50 California Representatives. The House votes on the top three Presidential candidates to win electoral votes, while the Senate votes on the top two Vice Presidential candidates.
In 2016 the Republicans won a majority in both houses of Congress, and also a narrow majority of state delegations. So assuming we get that same result in this timeline where Evan McMullin deadlocks the electoral college, it looks at first like Trump will be elected in the House, but since he was unpopular with the Republican establishment at the time, we might get a few anti-Trump Republican Representatives voting for McMullin instead of Trump, resulting in the House being deadlocked. Meanwhile Trump's running-mate Mike Pence should be elected VP in the Senate fairly easily, and if the House remains tied he'd become President. I can't imagine the Democrats in the House would like the sound of a President Mike Pence considering how conservative he is, so some may instead decide to vote for McMullin since he's a centrist anti-Trump outsider to prevent a Pence Presidency.
That's why I think McMullin would have been elected President if he won Utah and Clinton won Michigan and Pennsylvania (the two narrowest states in 2016). A McMullin victory in Utah was more likely than you may think because he was actually polling in the lead at one point and perhaps if he entered the race earlier he might have pulled it off.
