How to unpack std::tuple from C++ template?

Sure, you just need another level of indirection (as usual):

// this function declaration is used just for the type
// transformation, and needs no definition
template <typename... Types>
auto unpack(std::tuple<Types...>) -> std::tuple<std::vector<Types>...> ;

template <typename Tuple>
class MyClass
{
  // use the return type of unpack
  decltype(unpack(std::declval<Tuple>())) my_tuple; 
};

And now you can instantiate MyClass with a tuple, like this:

MyClass<std::tuple<int, double>> m;

which contains a field my_tuple of type

std::tuple<std::vector<int>, std::vector<double>>

Here's a working demo.

Yes, and to add to cigien's answer, another way to go about it would be to unpack it through a template specialization.

template<typename Tuple>
class MyClass;

template<typename... Ts>
class MyClass<std::tuple<Ts...>>
{
    // ...
    using VectorTuple = std::tuple<std::vector<Ts>...>;
    // ...
};