How does domestic demand affect the domestic currency's value
What effect is stronger in response to domestically motivated economic
  growth? Is it the depreciating effect of imports or the appreciating
  effect of new entrants or am I missing something entirely?


There's no general answer to that. It depends on the particulars of each economy. Some factors are:


Whether imports outweigh exports or viceversa;
Whether the tax reduction is coupled with spending cuts, tariffs,
foreign debt, etc.;
Taxpayers' general propensity to save the additional "disposable"
income could influence the exchange rate in either direction,
depending on where they deposit their savings.