Thermocouple probe insertion force

I got one of these:
https://www.amazon.com/exec/obidos/ASIN/B008S0K9KU/tvwb-20

REED Instruments TP-01 Beaded Thermocouple Wire Probe, Type K

Are the pins on the TC supposed to be entirely inserted into the connector on the TM?
It is very tight, and I didn't want to force it - thinking there was something awry,...

Yes they are a very very tight fit. Supposedly it is because the plug is forming not only an electrical connection but a thermal one so they are trying to get as much surface contact as possible. However, I feel like they are WAY too tight so I have jammed a tiny screwdriver into the + and - holes and bent the contacts a bit to make it easier. Be careful though because there's no way to bend them back if you go too far. The jacks are fairly resilient though so you'll most likely need several iterations of pokes before things feel smoother.

EDIT: Oh and yes they are supposed to go all the way in but you're going to get probably >99.9% of the same accuracy with them just touching the contacts.