Office for iOS wasn't _built_ under Ballmer. Outlook for iOS was _bought_ under Nadella, in the form of the startup Acompli.
The rest of the office-for-iOS suite took heavy inspiration from that, and didn't take a decent shape until 2016-2017.
The rest of the office-for-iOS suite took heavy inspiration from that, and didn't take a decent shape until 2016-2017.