Except the OP is talking about RPE at the same heart rates - not that HR is higher indoors.
This is what’s odd - you’d expect to see RPE go up in line with heart rate.
@JorritK is your outdoor riding off-road? Are you using your upper body more? Are you getting out of the saddle more? You might see a lower HR relative to RPE indoors if the way you’re riding on the trainer is very different to outdoors.
Also, are you riding with a power meter? If so, what kind of powers are you seeing at this HR indoors and out?
Edit: other thing that occurs to me is the gear you’re in and the type of trainer you’re using. If you’re in a low gear on the turbo trainer and/or the trainer has low inertia (i.e. it stops quickly if you stop pedalling), this can create a very different “feel” to outdoor riding as you need to be pushing all the way round the pedal stroke.