>> Upgraded firmware. Yes, on Nucleo Board it works.
Good to hear that
>> Is this the same for the standalone ST-Link adapter?
No, Standalone ST-Link V2 does not use this kind of starting sequence so it is not concerned by this problem,
this is specific to mbed enabled boards (which embeds ST-Link V2-1) ie. all Nucleo boards and some new discovery and eval boards
>> It also got a new version of firmware
Yes you can use the same upgrade executable to update your standalone ST-Link to V2J25S4