what do your dialogs look like when importing the .csv?
There is a choice of making the first row the field/column names. Those are not quoted.
But, yes! for the following rows, the content (except numbers) needs to be quoted in each column.
Importing by Tab-delimited does not have quoted columns (or comma-separated).
A way to 'test' is to stop at the column/field matching and "scroll" through the records that might be imported (the triangle-arrows). If you see there is a problem, don't complete the import.