How to split 1/2" OD male pipe for sink/dishwasher?
If you use that valve and your dishwasher starts leaking one day and your replacement takes a few days to arrive, you'll have no hot water to your sink. You should use a tee with a valve on each end of the tee so you can control the water flow independently. In fact, some cities require this. I learned this the hard way by failing my plumbing inspection by using the valve you linked.
The label you describe is kind of confusing. OD is typically used to describe pipe size, not fitting size. 1/2" FIP is used to describe pipe thread size. If 1/2" is indeed too large, maybe you should try a 3/8" sized fitting? Just to be sure, can you update the question with a picture of the label?
Finding copper/brass FIP/MIP fittings is going to be difficult and/or expensive. It might make more sense to buy a cheap cutter and get some shark bite fittings. Or if you want to be adventurous, solder it yourself..