If you swap specs in Undermine, your car will say you don’t have a boost applied and you need to visit the D.R.I.V.E. NPC. Even if you do that and swap boosts around, it still does not work until you swap back to the spec you were in when you got the car.
EDIT: Found a workaround. In each spec, you have to select a different boost, then mount the car, then change it back to the one you want. After this is done it should stick for every spec.