Character on rails ignores collision for some moments

Hi,

I have a made an 'on rails' Unity project, which is simply comprised of:

a first-person character controller with disabled controls (apart from looking around with a mouse) is a child to an object. This parent object is moved linearly via a series of waypoints when a button is pressed. The character, since it is a child, moves with the object.

However, there is a problem with collisions. If I go up the stairs, the character controller somehow ignores his collision detection for some moments and walks into the stairs. After a couple of seconds he repops up correctly onto them, however, occasionally the character even falls through! The picture below shows the process of walking into the stairs and then suddenly popping up to where the character is supposed to be. Is there a way to fix this collision problem? To somehow force the detection more, or some other?

I would not like to refuse the character controller's collision detection because then walking up the stairs is much more visually and tactilely pleasing than a static linear movement from waypoint to waypoint.

I would also like to state that I am not a programmer, I am an artist and I don't really understand JavaScript or programming. Although I do the coding myself on my Unity projects, but if there are difficult solutions to this issue, please do take the time to explain them so I could implement them.