The way a field is formatted on a layout is irrelevant here. What matters is the date format being used by the file. This affects data entry as well as importing.
The date format used by the file is either the short-date format of the OS under which the file was created (or cloned), or the short-date format of the current OS (depending on the setting in File > File Options… > Text).
From observation I've concluded the most often used date format is MM/DD/YYYY. However, the order is less important that the "YYYY" . . . yes, 4 digits. This seems universal these days. After importing data with two digit years I would run a script to update the data to four digit years. Also, to extract data using the "Left", "Right" or "Middle" functions, consistency of date format entry and storage is crucial.
My two cents . . .
I went to the File Options changed the toggles on all three and tried to import the same spreadsheet and it did not keep the current date field in FMP 9. It still went from YYMMDD to MM/DD/YYYY. Any other suggestions?
I am not sure we are on the same page: you can import a date in YYMMDD format directly into a date field only if your file is set to use the YYMMDD format. In File Options you merely switch between the file's saved format and the current OS format - but if neither one of them is YYMMDD, this won't help.
Perhaps it would be easier to import the date into a text field, and use a calculation to parse it out into a true date.