As a healer, I think you should try to assume that every tank will do big pulls. This way you are prepared for it. While its nice that some tanks will specify they are doing big pulls, it has become the norm and therefore most wont blink an eye and immediately will assume the healer can roll with it.

If you arent confident in your ability to handle large pulls (within reason) then I'd suggest making that known at the beginning of the party beforehand.

Ultimately should a wipe occur, I'm of the mindset that both healer and tank share the blame as either could have expressed their preference in the beginning.