Based on Jason Sebring's very useful tip, and on the stuff covered here and there, I found a perfect solution for my case:
Pseudo code with Javascript snippets:
immediately create a blank popup on user action
var importantStuff = window.open('', '_blank');
(Enrich the call to window.open with whatever additional options you need.)
Optional: add some "waiting" info message. Examples:
a) An external HTML page: replace the above line with
var importantStuff = window.open('http://example.com/waiting.html', '_blank');
b) Text: add the following line below the above one:
importantStuff.document.write('Loading preview...');
fill it with content when ready (when the AJAX call is returned, for instance)
importantStuff.location.href = 'https://example.com/finally.html';
Alternatively, you could close the window here if you don't need it after all (if ajax request fails, for example - thanks to @Goose for the comment):
importantStuff.close();
I actually use this solution for a mailto redirection, and it works on all my browsers (windows 7, Android). The _blank bit helps for the mailto redirection to work on mobile, btw.