Parsing rules can be arranged in any order via the Parsing Rules screen. To move a parsing rule to a different position, hover your mouse over the rule you would like to move, then select and drag the blue bar on the left until your rule is in the preferred position.
The order of your parsing rule will also be taken into account once you download your parsed data as e.g. a spreadsheet file. You can also order rules in the app to eliminate any post-processing.