No, you aren't required to move your current account to La Caixa.
But I did notice this little gem in the T&Cs.
Los Avios otorgados de conformidad con esta Parte A no son acumulables a los Avios otorgados a
los Socios de Vueling Club en el marco del Programa Vueling Club.
So you don't receive that much of a bonus for paying for your Vueling flights with this card.
In any event, if you fly Vueling a lot, this card might come in handy.