You don't say who manufactures the self-leveler. Although some underlayment manufacturers don't recommend their products installed over VAT, it can be done successfully.

You have to use the primer that will stick to the VAT. If this was Ardex K15, you would first apply their P-82 primer (P-82 will stick to almost anything).

Another way to approach your job is to use Ardex Feather Finish (or the Armstrong-branded equivalent). This product is mixed with water and then applied to the floor with a straight edge trowel and levelled (screeded) as you would regular cement. Yes, that method it quite a deal more work than straight self-leveler. Feather Finish also will stick to almost anything.

It is peculiar that the primer you are using is beading up...this leads me to believe that there is floor wax on the VAT, not just acrylic floor polish. Perhaps another round of cleaning with a wax remover might be in order.

I'm with glenn up here only I have one difference in opinion. I say accept no substitutions to the best, use either ArdexK15 with P-82, or even their EP-2000 if you don't mind working with epoxy, or you could try their Feather Finish, but if you're not used to concrete finishing style work, I would suggest self leveling. If you must substitute Ardex, go to Home Depot and buy Henry (you'll notice an Ardex logo below their name) because Ardex makes that brand as well.

Here is a link that might be useful: Ardex product listing

I also need to level a floor of the same type as mimiandalex. Another question ...this is for a kitchen and hallway, which have several doors to other rooms, and a stairway leading down to a basement. One of the rooms off the hall is a bathroom which has a tile floor lower than the floor that needs leveling, 4 other rooms off the hallway are carpeted. Would not the self leveling material run onto carpet, down to the bathroom tile, and down the stairwell? Can you use self-leveling for certain parts of a space, eg the very lowest parts, while avoiding other areas,eg under kitchen cabinets, top of stairwell, and transition areas (carpeted rooms, etc.)