I've had some of these post with no problem, others show up in the "earned" page but (a month later) still not show up on my statement, and others never show up as earned at all.

When I write in, the chat agents need a lot of help finding the offer, confirm the eligible charges, and then promise it will be posted in the next cycle. They don't post. I write in again, they say "one more cycle" or tell me to call. When I call, the agents again need a lot of help to find it, go away to talk to a specialist, and then come back and tell me to talk to the merchant.

Based on these experiences, I would certainly not shift any spend to a Citi card based on terms of an offer or buy anything based on the post-offer price -- they're just not reliable, and the process of following up is infuriating with no results.