Hello Pradyumna
We must make a distinction between the direction of user traffic, and the direction of BGP updates.
When we talk about applying BGP Local Preference, as an attribute, it affects which router will be used to forward outbound user traffic out of the local AS. This is referencing USER TRAFFIC.
However, when Local Preference is applied using a route map, it is applied on R3, and specifically on the BGP peering between R1 and R3 in an inbound direciton. This inbound direction references the BGP updates that R3 recieves from R1.
So the BGP updates to which a specific LocalPref is to be applied are applied on the incoming BGP updates, but the LocalPref values are actually used to direct outbound user traffic.
I hope this has been helpful!
Laz