I would not worry about the difference between 15mm (OD) and 1/2" (ID) they are very nearly identical.
For 3/4" (ID) the OD is 21.5 or thereabouts. The socketing tool will obviously work on 3/4" pipe. However the 3/4" pipe will be a very loose fit in a formed socket, this will probably work OK sine the pipe end will abut the socket deep inside but there will stikll be issues with the solder wanting to drop out of the fitting.
I've not tried one of these adgets as yet - I'm put off by the need to have to clean the formed socket where as (fresh) fittings come delivered spotless.