We've just completed and received the cash from a Citi bonus offer this past week. They are reliable, however you must follow all of the terms, keep appropriate minimum balances, and understand they will credit the bonus some period of time after you've met the time requirement(s). In our case, this was 60 days after completion (of a 90 day maintenance period). For yours, it indicates 90 days after the balance requirement is met for the package you sign up for.
We've also done another Citi bonus offer a year or two ago. Their eligibility disclosures always look the same as the small print you reference.
For your offer, it appears the only eligibility requirement is that you haven't had a Citi account in the past 6 months. However, you must follow the steps indicated in order in the "Eligible Customers must:" section.
I would not deal with the Citi reps by calling. Simply print out the offer page, save it, and refer back to it later if they do not give you the bonus 90 days after you meet the balance requirement. Again, be sure that you follow the steps in order as they've shown them. If at any time you have questions, simply use the Chat feature within your online account - the folks there can look up any information you need, verify the account is properly associated with the bonus offer and answer any questions you have regarding the bonus offer. So, you could apply, open the account, then go to Chat within the account and ask your questions before even transferring any money in. I use the Chat after the bonus is paid, I empty the account, and tell them to close it. They take care of it and confirm immediately.
From the looks of it, the $300 bonus for $15,000 gets the best bang for the buck. Though having to open two accounts to do it is more work. For the one we just completed, it was $200 for $5000 for a single basic checking account.
