Agree with novocaine, that's what I was taught too. There is OFTEN (not always) a slot in the quill (female), shaped to take that tang, so as novo says, did you (before pushing it fully home) try gently rotating it to see if it suddenly "popped" further in? If so, your quill does have that slot, but as above, many machines don't, that's why you can buy them with and without tang (and also why a lot of people cut the tang off, it's normally quite soft, not hardened like the taper portion).
BTW, I don't want to teach Granny to suck eggs, but EVERY time you remove and replace a MT (e.g. fitting and removing a drill chuck into the tail stock on a lathe, or tooling on a mill), you should wipe the male part off with a CLEAN rag/tissue/fine brush, and ditto, up into the female bore. Although hardened, a small bit of oily swarf hanging on (or hiding up the bore) when fitting a MT WILL leave a minor indentation on the female bore (it's a good trick to look for scratches & digs in the female bore when buying any SH machine tool - shows how careful the previous owner/s were/not).
HTH
AES