This is incorrect.
When it comes to "burden of proof", what matters is who is making the claim FIRST, regardless of whether that claim is the non-existence or the existence of a supernatural Being, unicorns, or whatever.
The burden of proof falls upon "the one making the initial claim in the first place."
If you make the claim of the non-existence of God then the burden of proof rests upon you to scientifically show replicable tests this is so.
However if you make the claim of the existence of God, then the burden of proof rests upon you to scientifically show replicable tests that this is so.
It all depends on who is making whichever claim first. The burden of proof rests with that initial person.
We have had this argument before and I gave countless examples and definitions of this fact backed up by references on the internet.