Consulta de suma de Mysql que devuelve un resultado incorrecto cuando se usan combinaciones múltiples

Use los totales directamente porque sus uniones probablemente creen más filas en combinación de las que desea.

Prueba lo siguiente:

SELECT id, MAX(Total) as FinalTotal ,MAX(Payment) as FinalPayment
FROM si_invoices a 
    left join 
    (select invoice_id, sum(total) as Total from si_invoice_items group by invoice_id) b 
    on a.id = b.invoice_id
    left join
    (select ac_inv_id, sum(payment) as Payment from si_payment group by ac_inv_id) c 
    on c.ac_inv_id = a.id 
group by id

o si la identificación es única:

    SELECT *
FROM si_invoices a 
    left join 
    (select invoice_id, sum(total) as Total from si_invoice_items group by invoice_id) b 
    on a.id = b.invoice_id
    left join
    (select ac_inv_id, sum(payment) as Payment from si_payment group by ac_inv_id) c 
    on c.ac_inv_id = a.id