Dear Alessandra,
Like other Joomla module, you will need to have module position to add JA Promo bar module to. However, by default, there is no module position in the offline page so you can try with my workaround as below (I will take our Purity III template as example):
1. Create a new module position called offline_promobar
You will go to file: templatespurity_iii(your default template)templateDetails.xml and add a new position inside <positions> tab, it will look like this:
<positions>
<position>offline_promobar</position>
<position>languageswitcherload</position>
<position>head-search</position>
<position>mainnav</position>
................................
2. Call this new module position in offline page
You open the file: templatespurity_iii(your default template)offline.php and add this line of code inside <body> tab
<body>
<jdoc:include type="modules" name="offline_promobar" />
<jdoc:include type="message" />
................................
3. Module assignment:
Access administrator are of your site, navigate to Extensions > Module manager > JA Promo bar and assign this module to new offline_promobar position you just created above and also check the menu assignment tab to make sure that you assign to all pages.
Hope this helps