Once a student enrolls in a course in Axess, the student will typically be added to the Canvas site within 24 hours. Canvas processes 500 updates/changes per hour, so the number of updates in the queue will affect how quickly the student is granted access to Canvas.
Often, students who have been added to Canvas do not see the course on their Canvas Dashboard, so they assume they do not have access. This can be because the student had "favorited/starred" courses to appear on their Dashboard previously. To include or remove courses from one's Dashboard, steps can be found in the help guide, How do I customize my course list?.