It is not required, but it can be helpful to have screeners working at similar times because in some cases (if you are dual screening, meaning each reference must be screened twice), one screener may screen many more references and then other screeners have to "catch up." It can sometimes cause confusion because the person who screens many more references will see the 'you can stop screening' message although the group has not yet reached the 95% estimated recall point, since a number of references still need to be screened by a second reviewer, and this remaining screening may generate conflicts and affect the model and also estimated recall.
It is also possible that if one screener screens many more references than other screeners that you could end up screening past the 95% estimated recall point in order to catch up and complete dual screening all references.