At first sight, it would seem that somebody, if not everybody in the Cal Crutchlow saga must be being a little economical with the truth. Maybe not. It is possible to construct a timeline that accommodates the known facts.
We'll start with World Ducati weekend where Cal announced on stage that he was staying with the red team. In other words, he was exercising the option is his contract that gave him an extra year. As this happened on a Ducati stage with all the top management present, I don't suppose this was a surprise to them.
Meanwhile, Lucio Ceccinello's LCR team secured a deal with a new sponsor and offered their rider, Stefan Bradl, a new deal. Unfortunately, Stefan had taken notice of the whispers and jumped ship; he'd already signed for Forward Yamaha. There's the late job offer that Cal has mentioned. All that was necessary was for Cal and Ducati come to an arrangement over that contract. As neither party was desperate to continue the relationship, I doubt that was too difficult. Did any more money change hands to expedite the deal? I don't think so. It is unlikely Crutchlow's side would endanger the deal by trying to screw more money out of Ducati; that would be a dangerous game.
It's more likely that a scheduled on-signature payment was made and now everyone's decided to stick their hands in their pockets and whistle until the end of the year.