Add 2nd column header to Matrix

I've edited this post since the model works with an active relationship between the tables

Sure, here goes.

1) You need to create a table which will allow for the column structure of the matrix. This you can create in Power Query which will furthermore make it dynamic. Basically you need a table referenced to the fact table and add a conditional column which returns "Budget" if the row for "Actuals" is blank else "Actuals"

This is the M-code I've used

let
    Source = Table,
    #"Removed Columns" = Table.RemoveColumns(Source,{"dimension", "Budget"}),
    #"Added Conditional Column" = Table.AddColumn(#"Removed Columns", "Calculation", each if [Actuals] = null then "Budget" else "Actuals"),
    #"Removed Columns1" = Table.RemoveColumns(#"Added Conditional Column",{"Actuals"}),
    #"Removed Duplicates" = Table.Distinct(#"Removed Columns1")
in
    #"Removed Duplicates"

to get

2) Set up a relationship between the month fields:

 3) create simple base measures for actuals and budget

Sum of Actuals = 
SUM(Table[Actuals])

Sum of Budget = 
SUM(Table[Budget])

4) Create the final measure you will be using in the matrix

Final matrix measure =
SWITCH (
    SELECTEDVALUE ( 'Matrix Header'[Calculation] ),
    "Actuals", [Sum of Actuals],
    "Budget", [Sum of Budget,
    SUMX ( 'Table', IF ( ISBLANK ( [Sum Actuals] ), [Sum Budget], [Sum Actuals] ) )
)

5) finally set up the matrix visual using the whatever field for the rows, the fields from the 'Matrix Header' table as columns and [Final matrix measure] as the values. Format the visual to your liking

I've attached the sample PBIX file for you