Can a road bike BB work on track bike?
Bottom brackets are incredibly confusing--there is a huge number of standards, and some of them refer to the diameter in the name, some the width, etc.

The compatibility chart for your new crankset lists BSA as an option. BSA uses the same bottom-bracket threading as JIS--which we know is already working on your bike--so that is the correct BB to get. What you'll be getting is just a set of thread-in cups and bearings, rather than the cups, bearings, and spindle as you had on your old BB.

Italian bottom brackets are also threaded, but the thread pattern is different. And the other BBs that the crankset is compatible with don't use threaded cups at all.