Documentation says Firefox should be ok with LastModifiedDate, but it's not. It's consistently being set to 1/1/0001 12:00:00 AM, which is not useful.
Happens in any RadAsyncUpload example if you look at the value for LastModifiedDate in the AsyncUploadedFile objects.
Works fine in Chrome, Edge. Fails in Firefox for Mac or Windows.
The fix is in QA stage, and if there are no issues, it will roll out with the R2 2019 release.
What I can see is that the AJAX request for the file upload does not contain the parameter for the last modified date. When we are creating the xhr request object, we explicitly check for the presence of the last modified date field in the file object before adding it. Unfortunately, back when the FileAPI module was implemented (if I recall correctly, around 2011), the field was lastModifiedDate and this is what we check for. It seems that at some point FireFox has stopped supplying this field and only provides lastModified. So, the check we have at the moment now cannot find the date from the file.
I am logging this for fixing and you can track its status in the following URL: https://feedback.telerik.com/aspnet-ajax/1389463-firefox-63-and-lastmodifieddate. This is the page at which I made this report public so other people can also see it. I have already added your vote and you can get notifications on status changes by using the Follow button. You will also find your Telerik points updated for reporting this.