This continues to be a problem for me as of the latest open beta.
Attached is a very simple .miz file with an F-16 departing warm from Incirlik with one AI wingman. On a dedicated server, the AI wingman does not move, even after the player has taken off.
In single player, and also with the server built-in to the DCS client, the AI begins to taxi as soon as the player starts moving. It is only on the standalone, dedicated server running separately to the client that the issue occurs. I'd just like to check with @BIGNEWY that when you tried to reproduce this, you used a dedicated server and not the built-in server? As that might explain why the issue didn't occur on your end.
WingmanTest_Incirlik.miz