No, they definitely don't have that instinct. I've had baby bunnies try and take a 5 foot leap off my shoulder. So you definitely need to do something to stop them from being able to access the ramp until they are at least 4 weeks old. I think others with this issue have either moved the bun to a lower floor or closed off access to the ramp temporarily.
I know that it will then restrict mom from using the run, so you could try to just to let mom out into the run for parts of the day(with food and water access, litter box, and places she can hide if something spooks her) while you continue to block off the ramp, then return her to the main part of the hutch in the evening and night so she can be with the babies and nurse them. She doesn't need to be with the babies all day as moms generally ignore the babies until it is time to feed them, usually once or twice in the morning and/or evening. Once the babies are old enough to leave the nest(2-3 weeks old) you could also start to let them have short periods in the run with access to a box with hay they can nestle into when tired, but not too long if there is grass in there as you want their digestive system to gradually get used to eating fresh grass, and you may need to supervise their play time at first to make sure mom is ok with them being there and that they are ok and can't escape the run by squeezing through the bars if there is wide spacing.
If that doesn't work out, another option is to bring the babies inside with you in a nesting box when it's not their nursing time, to give mom time to be able to access her run. The risk with that is sometimes it can upset the mom, so you would just have to gauge her response. The mother rabbits I've dealt with always liked getting a break from their babies, and didn't mind me handling them.
