For all who have problems with this:
Go to your WordPress installation wp-content/plugins/acf-accordeon/js/input.js
there in the line 33 you change:
$(this).nextUntil(".field_type-tab, .acf-field-accordion").wrapAll('<div class="acf-accordion-group"></div>');
into
$(this).nextUntil(".acf-field-tab, .acf-field-accordion").removeClass('hidden-by-tab').wrapAll('<div class="acf-accordion-group"></div>');
So accordeons dont eat tabs and also show the content in them. Works at least for ACF 5.3.4 Pro. Not sure if ACF 4 uses the same classes, if not change acf-field-tab to the class of a new comming tab and hidden-by-tab in the class that hides tab content. This is the cleanest sollution. So no !important or css things.
If the creator of this plugin reads this. Was a honor to help.
Sorry for my bad english its not my mother tongue 🙂