It’s better having a numerical value, or an abbreviation
Quoting biblatex manual:
This must be an integer, not an ordinal or a string.
In JabRef, we nevertheless decided to go for abbreviations, which did not cause trouble on our side:
month = jun,
To achieve that, press Alt+F8 or Quality -> Cleanup Entries... Then, following dialog appears:
If the contents of "Run field formatter" look different, just press "Recommended for BibTeX".
With File -> "Switch to biblatex mode", one can switch to biblatex mode and then have "Recommended for biblatex".