Keep these records for tax purposes if fee takes a tumble? (8)

'keep these records for tax purposes' is the definition.
The definition suggests an adverb but the answer is not.

'fee takes a tumble?' is the wordplay.
'fee' becomes 'pays' (I can't explain this - if you can you should believe this answer much more).
'takes' means one lot of letters goes inside another.
'a tumble?' becomes 'slip' (tumble is a kind of slip).
'pays' placed around 'slip' is 'PAYSLIPS'.

'if' is the link.

Can you help me to learn more?