Also I noticed on the 707 you have to turn the autopilot mode select knob once and back to HDG, otherwise an INS programmed course change will not happen.
That indeed sounds something strange since the 707 does fine on "Nav" with the Civa. No back and forth with the "HDG" mode necessary.

I used HDG mode like the tutorial told me, but in the 707 its the darn NAV MODE i need
Are you speaking of the general Civa tutorial there? Well, some planes use the Nav mode, others stay on the heading one.
But the 707 manual states the need for "Nav" I think.