doesn't sound right to me at all.
The top mount should be fixed securely to the top of the strut. If it isn't, you're doing it wrong.
Above the top spring cap, you need the top mount bearing, then followed by the top mount, then the first retaining nut which holds it all on.
Then it goes up into the arch and through the turret, and the top cap goes on under the bonnet, followed by the second retaining nut.