A share falls by roughly the dividend on the ex-date. A CFD holder does not own the share and receives nothing from the company, so without an adjustment a long would simply lose the dividend and a short would pocket it for free. The broker therefore posts the cash equivalent.
Treatment is asymmetric at most firms. Longs typically receive the dividend net of a withholding-style deduction on foreign shares, while shorts are debited the full amount. That gap is a real cost of holding a short across an ex-date.
Index CFDs get the same treatment in aggregate: as constituents go ex-dividend, the cash index falls and a corresponding adjustment is applied in proportion.
Example: long 1,000 CFDs on a share paying $0.45. The price falls about $450 on the ex-date and the account is credited around $450, or less where a deduction applies. A short is debited the full $450 while gaining $450 on price.
Related: share-cfd, index-cfd, cfd-corporate-action-adjustment, overnight-financing-charge