When you try to add Alternate Layouts using the Twixl Publisher tool Alternate Layouts, no Alternate Layouts are being generated. You get no error-messages.
This is caused by a rather messy bug in InDesign when you have duplicate names in your Text Styles and selected Copy Text Styles to New Style Group as an option in the Twixl Publisher Alternate Layouts panel.
E.g. you are using the same name for a Paragraph Style and a Character Style.
One or more styles were not mapped. Cannot create a mapped style when one of the source styles is based on another source style (OK).
This InDesign-error has in fact nothing to do with "based-on"-styles at all.
Just rename one of your Text Styles, so you no longer have duplicate names.