This article is complete and utter BS.
Incirlik AB (not AFB, a designation only used on US soil, the first of many errors) is a Turkish installation that they have agreed for decades to allow US and NATO to use for specific purposes.
Erdogan is settling scores with known, suspected, or just untrusted Turkish military across the country, to include Incirlik. US and NATO personnel are now caught in the middle of the purge.
Incirlik is too useful to NATO and the US to abandon unless the situation in Turkey descends into civil war. Erdogan is not so stupid as to move directly against US and NATO personnel. His focus is his real and imagined Turkish enemies. That this causes inconvenience to our folks is probably a bonus for him, but not his objective. He needs to consolidate power and prevent organized opposition.
As to nuclear weapons, the US government will neither confirm nor deny their presence. While the facilities exist for them, no one will say if they are there.
If they are there, commanders on the scene have inherent authority to defend US property and personnel with any means at their disposal. No one, to include the President, has the authority to order the surrender of people or weapons not under their control.
Which is why the Navy is hammering the leaders involved in the boat fiasco with Iran. The Coast Guard similarly hammered an Admiral and Captain in the ‘70s for allowing Soviet goons to capture a defector on a cutter. The Army did not prosecute Wendel Fertig and Russell Volkmann for disobeying surrender orders, promoting themselves, and organizing their own armies in the Philippines from 1942-45.
There is no evidence the nukes have been moved at this point in time. Erdogan needs to reestablish his defense forces before he could make that move. Otherwise the Russians will just nuke the entire facility as the nukes are leaving.