Expenses affect your client recoverable expense accounts (if you use the Cash accounting method) or WIP (if you use the Modified Cash or Accrual accounting method).
If the firm uses Cash or Modified Cash accounting method, then when you post an expense entry to a client file with an expense General Ledger account and then post a firm check to the expense account to pay for the expense, the net affect is a debit to your WIP Expenses and a credit to your general bank. The net affect on your client expenses is zero unless you pay out more or less than what was charged to the client. For example, if you post a $100 expense to the client but pay $150 with a firm check, there is a net expense to the firm of $50. The client recoverable expense accounts in your General Ledger reflect the recovered client expenses.