As part of yesterday's insurrection response, [VA Governor Northam sent his National Guard into D.C.](https://www.wsls.com/news/virginia/2021/01/06/gov-northam-sending-virginia-national-guard-and-200-state-troopers-to-washington-dc/):

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> Virginia is sending reinforcements to help law enforcement in Washington, D.C.
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> Gov. Ralph Northam announced on Wednesday afternoon that he is mobilizing members of the Virginia National Guard, as well as 200 Virginia state troopers.
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This sounds odd to me because [the National Guard in D.C. is under the President's command](https://politics.stackexchange.com/questions/61472/what-authority-does-the-vice-president-have-to-mobilize-the-national-guard).

How does this work in practice? Could a state governor order their National Guard troops into another district/state, and because those orders have been given they stay in effect, or when the NG unit crosses the administrative border, are they subject to the local civilian commander in that region?