The issue is, that the cell is selected, but the UICollectionView does not know anything about it. An extra call for the UICollectionView solves the problem:

[collectionView selectItemAtIndexPath:indexPath animated:NO scrollPosition:UICollectionViewScrollPositionNone]; 

Full code:

- (UICollectionViewCell *)collectionView:(UICollectionView *)collectionView cellForItemAtIndexPath:(NSIndexPath *)indexPath {
    UICollectionViewCell *cell = [collectionView dequeueReusableCellWithReuseIdentifier:@"Cell" forIndexPath:indexPath];
    cell.selected = YES;
    [collectionView selectItemAtIndexPath:indexPath animated:NO scrollPosition:UICollectionViewScrollPositionNone];
    return cell;
}

I keep the question to help someone who may face the same problem.