Perhaps it's like most other things in life. In hindsight, we might have done it differently.
In this case, there are probably better, more descriptive (and less confusing) adjectives than "fictitious" which would succinctly describe a non-existent but perceived (or imagined) force.
Even so, I never visualized something pushing me back into the seat. I always visualized the seat pressing against me. After all, I didn't feel sensations on the front of my body when accelerating. The sensations are the same as if someone has come from behind and starting pushing you.
Removing yourself from the equation makes it easier to see: imagine a ball on a string in a car. Something happens and the ball moves forward relative to you. It’s not hard to see how you might assume a force pushed the ball forward.