We support all modern/evergreen browsers. The browsers supported are listed here.
Animator Core (the rendering engine + interactive runtime) does not support IE 11. It was a tough call when we chose to support evergreen browsers only, though IE11 simply doesn't have the capabilities needed to support the things you can do in Animator.
A fallback could be handled with user agent checks in your website (e.g. if modern browser, show animation; else, show something else).
Any discrepancy between [Preview] mode in Animator, and a published project on share.haiku.ai should be rare— if there is, it’s likely browser related. Send us a link and we can look into it.