If the pt member pulls a mob when the PLD has no MP, regardless that PLD better be up and ready to voke the mob off him the moment the pull macro goes off. The longer you take to do this, the longer the mob will have to remove shadows (if the puller is subbing /nin) and the puller will start taking dmg, which ultimately is going to mean that the healer will have to toss out more cures, resulting in less MP to continue chains, which means less xp.
If hate isn't kept because she doesn't have MP to be casting anything, then that would be the puller's fault for not allowing a couple of seconds of rest, and then it becomes her responsibility to tell the puller to slow down a little.
That being said however, considering a PLD is the top tanking job in the game (meaning they can keep hate the best) there is no reason why she shouldn't be able to get hate back if it is lost, because at the very minimum the provoke ability is only a 30 second recast. PLDs have a lot at their disposal to regain hate and keep it on them, and considering it was an Aht Urghan area, having the refresh added with the sanction effect + auto-refresh, MP will be regained quick enough.
I've been in parties where the puller has pulled a little too quick for my preference, but if the chains can be kept up and hate isn't passing to the DDs for more than a few seconds then I'm not going to complain, but instead adapt to the lower pool of MP. But then again i'm also Elvaan so dealing with low MP is already something I have to be on top of. When needed, you have to adapt to the pace of the party if its not going to hinder the xp/hr.