Help me solve a dispute- do the secondary lords pay taxes to their Lord Paramount lieges?

It’s not entirely clear how taxation interacts with the process of subinfeudation, and it’s not helped by the fact that when we see lords interacting with their vassals, it’s almost always between immediate vassals. 

The only clue I can think of is that the Redwynes have to pay excise taxes on wine to the Crown despite being vassals of the Tyrells. That may suggest that lords pay taxes both to their immediate liege lord and that lord’s liege lord, or that the Redwynes are a special case because they are directly exporting goods to foreign countries on a scale that most vassals wouldn’t.