If they're suddenly asking you to log your hours, they're looking for a reason to terminate/replace you.
Don't attribute to malice that which is adequately explained by stupidity. A previous job made us track our hours so that we could "improve estimates," but mostly it only made people unhappy.
We ask all of our employees and contractors to track time against tasks. Yes it can be a pain but it helps prevent people from spending way more time on a task than there was budget for.