I think Nick was overthinking.
And I was a bit confused as to why Joe, who was totally sure Nick was a faithful, didn’t tell him that he’d pretended to team up with Alan and Cat, and told them he’d vote out David. I think that was Joe’s error - not telling Nick the plan, which meant Nick started overanalysing it all and wondering if Joe was also lying to him.
What would they have done if Nick had voted for Alan instead of Joe at that last vote? Surely a tie at that stage in the game wouldn’t have been broken by effectively a coin toss like earlier in the game?