I can only test it in Adobe software, as it's an Adobe font. The problem is the same in Indesign, Photshop and Illustrator. I can fix it by creating outlines, but that's only a possible solution in case of short texts.
This is an unfortunate side effect of some script fonts, especially if you're custom-kerning characters together to give the impression of perfectly flowing script.
I'm getting the idea that you're looking for someone to confirm there is a problem with the font. From previous experience, I can confidently assure you there is. You're also looking for a solution, which you've already come up with: Convert To Outlines, then use Pathfinder tools to Unite the script characters to create your flowing script effect.
There really are no better answers right now: yes, there is an issue and yes, there is an effective workaround that corrects for it. If you're using this font for large blocks of body type that may introduce complexities, But if you're using it for display type it's not an issue you can't easily overcome. You may find better results with large blocks of type by doing your fixes in Illustrator, then placing the resulting .ai, .pdf or .eps file in your InDesign document.
I wish I had a better answer for you, but I believe this is the best course of action for you. We're end users, just like you. We don't have the ability or the authorization to redesign and repost your Alicia font for you.
Hope this helps,
Randy