The externality applies to residents who do not take public transit too. The two decisions should not be coupled.
If you want to do a Pigovian tax, do a Pigovian tax properly. If you want to do congestion pricing, make it budget neutral to users. If you want transfer payments, do that and call it that.
If you want to do a Pigovian tax, do a Pigovian tax properly. If you want to do congestion pricing, make it budget neutral to users. If you want transfer payments, do that and call it that.