You are required to report any income you receive from Casa Shares on your tax return.
Casa Shares will send you the corresponding summarized tax disclosure form (specifically a 1099-DIV) for your investment by the end of January of the following year, so that you can file your taxes appropriately. Investing in states that you don't live in will not trigger additional tax filing requirements. Any relevant state taxes would be based on the state where an investor files their tax returns, not where the property is located.
Note: Vacation rentals do not qualify as a REIT. But they are still taxed as a Corp so they are treated the same way in this respect.