Why did my deck membrane fail?
Usually movement, ponding water or a detail at an edge or penetration rather than the membrane itself. That is why a quote for recoating without looking at the falls and flashings is one to be careful with.
Is this the same as what a tiler does?
Overlapping. Tilers routinely waterproof showers as part of tiling. A dedicated waterproofer is who you want for decks, balconies, basements and anything that has already failed.
Will it be certified?
For a bathroom it must meet the building code and you should get documentation. For a deck, ask what warranty covers the membrane and what covers the labour, since they are often different lengths.
Do the tiles have to come up?
For a failed membrane under tile, usually yes, and any quote that says otherwise deserves a question. That is most of the cost, which is why the investigation is worth paying for first.