This mod may be able to force the ordering:

'SELECT number, date, miles, purpose
FROM mileage
WHERE date BETWEEN ? and ?
ORDER BY 2'

If that doesn't work, try:

'SELECT number, trunc(date), miles, purpose
FROM mileage
WHERE date BETWEEN ? and ?
ORDER BY trunc(date)'

because date formats are strange and they often contain unfathomable data!

@ncientgoose