Ok so, I managed to find out what's wrong here. I reckon it's a bit tricky x)
The idea is to force the position sample on the Shape to be always in world space, and this is achieved by using a different spawn function than usual : the PostEval function. Set your Spawner Script like so:
And inside UE4, set up your Shape Sampler like this:
By letting your sampler unparented and with 'Use Relative Transform' unticked, your emitter will always sample the true world space position of your shape, even if you are moving either the Emitter actor or the Shape sampler :)
Let me know if it helps !