StorageEngineUsed set to TabularMetadata. For databases in this mode, you must use Tabular APIs to administer the database
It sounds like you are trying to process your tabular model (which is of version >= 1200) with XMLA script (so all in all command is in XML). That kind of tabular model has to be processed with JSON command. I had the same error message and it just turned out that I was trying to refresh the newer tabular model (of version >=1200) with XMLA command. After using JSON command - it all worked. Probably for some reason while moving the tabular model from one server to another - the version of that tabular model was somehow upgraded to >= 1200. Or you are using old SSMS which is only capable of producing XMLA commands.