No, not everywhere.
In postdoc, you will be consider only if you have already publish your quality paper in reputed journals and in English. So, in most of place you don't need English proficiency test.
If they need, they will check your English speaking test in Interview.
In some European and US universities, they ask language test to make their shortlisting easy.
So, for postdoc, you should give more attention for publication and your writing ability.
If your publication is good than your chance will be more to get successful Postdoc position.
For postdoc you should not give more attention to language proficiency test.