There is no time frame for the IRS to send a notice to an individual. Once they start processing your return and run into an issue. They will notify you if necessary.
Turbo Tax will not have a status on your refund. If the IRS website says processing, this means they are working on it. Please use this link to track your refund from the IRS. https://www.irs.gov/newsroom/use-the-wheres-my-refund-tool