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FICO scores update daily, but utilization changes are only reported when the statement closes.
Statements usually close 2-3 days after the payment due date but this isn't always the case, you'll have to check the date on your previous stataments to get an exact date. I'd guess though that your Citi DC will close on the 6th or 7th of next month and if you're able to pay off the balance transfer amount by then, then your scores will not take a hit as you're hoping to accomplish.
You should do the balance transfer ASAP though if you want this to work, they can take about a week to process and if it doesn't go through before your Cap1 statement closes, then you'll have to wait until next month's statement to report a lower balance.