I'm not seeing your pictures either, but Taig never offered mills with a ER-11 spindle. So either you're mistaken about the size of yours, you're inserting the collets incorrectly, or you've got a mill that someone customized with an odd spindle they found somewhere.

I'm guessing it's the middle mistake. The closer nut won't screw on correctly unless the collet is snapped into the nut first, before the tool is inserted. It will give a click, and then won't fall out if you invert it. Try that and see if things don't work better.