We all have our own personal "twist" on how we see the cards, personal meanings. When getting a reading from another tarot reader who do you think the cards are giving the message to.
To the person who owns the deck and who is doing the reading.
but when the sitter is seeing the cards they are picking on things as well.
Unless I am specifically teaching or mentoring someone, I try not to do that. THEY are the reader, I have asked for THEIR take. It would simply be rude of me to put my own interpretations on their cards, because the deck may have had decades of having different meanings to mine assigned to those images.
Respect what your reader says, or don't get a reading from them.
Or, as I said, if they are a student by all means offer suggestions that flesh out their meanings of the cards, but if they are doubtful, go their meanings, too. The deck is theirs, it is speaking to them, not to you.
I have a young Tarot-guy whom I mentor (he turns up here, occasionally, as NisabasAcolyte) and sometimes he's quite good as a reader and sometimes he is truly awful (aren't we all?).
We both own a copy of the same deck. One day when we were having a Tarot-based get-together, we both had our copies of that deck with us, and both of us still had it in its original box. There were other decks scattered around, too. At the end of the evening when we were both packing up to go home, we picked up our other decks, and these two were left on the table, neither of us were sure which copy belonged to whom.
So we took them out of their boxes. I picked up one copy. It felt normal. I picked up the other. It felt somehow wrong. I spread out a few cards. They made no sense. It was his deck because it didn't feel like my deck and its images made no sense to me even though it was the same as mine.
So accept the reader's reading. Not all readers are good readers, but all decks speak to their own owners, not their owners' clients.