The SMD connector is for cables with a laminated backup tab and .30mm thick. The touch screen photo’s show what appears to be such a cable, but the cable on the screen just received has no laminated tab and is only .10mm thick so, as you said, the connector can’t grip it and it simply falls out.
I wrote to tech support and the person replying said he was able to get the connector contacts to make a connection, however a bit of force was necessary. The only force I can see making a difference would be to squash the connector by .2mm, but this would likely provide a very unreliable connection, if the connector wasn’t simply destroyed in the process. A better choice would be to apply something .2mm thick to the backside of the end of the cable, but the best would be to simply get and use a proper connector designed for .10mm thick cable.