It IS as simple as pushing the wires in, but you need the correct tool or it will be an exercise in frustration and you likely won’t make as reliable a connection (then the new connector may overheat too, due to excessive resistance).
The Marco page linked above has several of them; the cheaper punch tools work fine, but if you have a lot of connectors to replace it might be worth investing in one of the C-clamp style units as they are a little easier to use and quite a bit quicker.