Here is how you can make an assertion on a nested call to another class:
let(:double) { instance_double('something') }
before do
allow(SomeClass).to receive(:some_method).and_return(double)
allow(double).to receive(:another).and_return(true)
end
it 'does something useful' do
subject.call
expect(SomeClass).to have_received(:some_method).with(args)
expect(double).to have_received(:another).with(other_args)
end