At the corners of the center dots, 2 and 8 will always be diagonally opposite to each other and the numbers 4 and 6 will be diagonally opposite to each other. These two digonal sums will add upto 15 since the number 5 is always at the center at R5C5.
Let us take yesterdays Magic Square Sudoku for example. I have updated the pencil marks for the centers.
Now let us look at R2C8. Since the only even number that can fit there is 8, we also get the number 2 at R8C2, so that the diagonal sum is 15. That leaves us with options 4 and 6 for R2C2 and R8C8. Since number 4 already exists in Box 1, we can safely place number 6 in R2C2 and number 4 in R8C8. so we have placed 5 numbers till now and we have the diagonals in place. Diagonals here meaning the centers.
Now we can fit the odd numbers as per the sums of each row of centers. We have 6 and 8 as the two centers in R2. So in order to have a sum of 15 we can safely place the number 1 in R2C5, 7 in R5C2, 3 in R5C8 and 9 in R8C5. Once all these 9 digits placed, the sudoku can be solved like any other Classic Sudoku.