**Update:**

Based on your updated question I guess you want something like

    Manipulate[{a, b}, {a, 1, 10}, {b, 1, 10},
     Button["export", Export[SystemDialogInput["FileSave",".txt"], {{"a", a}, {"b", b}}, "Table"], 
      Method -> "Queued"],
     Button["import", {a, b} = Import[SystemDialogInput["FileOpen", ".txt"], "Table"][[All, 2]], 
      Method -> "Queued"]]

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**Old post:**

You could use a [`Setter`](http://reference.wolfram.com/language/ref/Setter.html?q=Setter) instead of a `Button` to get the intended scoping

    Manipulate[Plot[Sin[x (1 + a*x)], {x, 0, 6}], {a, 0, 100}, 
     Dynamic@Setter[Dynamic@a, ToExpression["a=90"], "a=90"]]

One can make the `Setter` looker like a `Button` by adding the option `Appearance -> "Button"`.