In the frame of a 'block universe' we all perceive the present at the same time. Imagine astronaut that goes to deep space and when he comes back he starts experiencing things ahead of time.
EDIT: As per request in comments: let's say he is in a time frame that is ahead one minute from the universal.
I believe it is also worth expanding on what 'block universe' means for those who are not familiar with theory.
This is a doctrine called determinism. Main idea is that since all physical objects obey laws of physics and that everything is predefined including your thoughts and future behavior. This can be seen as a Universe where from the beginning to its end it is like a movie that has completely made with every event existing in its own movie frame. It can be observed at any point in time. For example this edit you have already finished reading it - it's just that you from your perception of time haven't reached this point yet. For character it would be one minute ahead of others since he is desynchronised from normal frame of 'now', so he could start reading my edit one minute before I would finish writing it....
How could desynchronization from others with regard to experiencing present manifest itself?