API-TC LOW ASH, avoid TCW3 and any "all-purpose" 2-stroke oil.
If you're using the factory oil injection system, you need to clean the tank, line and replace oil strainer filter first, if it's been filled with the wrong oil b/c mixing the correct and wrong oil will cause the mixed remnants to become gelatinous and will clog the injection system. The reason is, the detergent package used in other 2-stroke oils is incompatible with the API-TC detergent package.
The wrong oil will be anything that's designed for outboard engines, usually TCW3. The correct oil is API-TC LOW ASH, mineral or synthetic.
If I was running a 587 motor, I would probably use a mineral or blend API-TC LOW ASH but the synthetic API-TC LOW ASH version is another choice some folks prefer. Synthetic can handle more heat before decomposing and the larger engines require it. Personally, I don't believe synthetic provides the same level of downtime corrosion protection that mineral does.
If you plan to use the engine hard, synthetic lubrication should outperform.
XPS2 is the seadoo original equipment brand.