Assigning value to cells with Excel VBA
The short answer is: 

Don't use vba, use a formula. In particular, a combination of IF and SEARCH. 

=IF(SEARCH($A1,"Admin")&gt;0,"Exploitation","")


But this is code review, so let's do that anyway. 


Regex is slow. It seems that you're only using it for it's case insensitivity. Given that, you can directly compare cell values by using StrComp with the vbTextCompare option. (useful article on StrComp)
i and j are typically used for loop counters, but row and col make more sense in this case. 


Here is what this could could look like:

Dim row As Integer
For row = 1 To 10 'let's say there is 10 rows
    Dim col As Integer
    For col = 1 To 2
        If StrComp("Admin",Cells(row, col).Value,vbTextCompare) Then
            Cells(row, col + 1).Value = "Exploitation"
        End If
    Next col
Next row