Speed limits are set by ORS 810.180, which basically says that a road authority may set a speed limit. The DoT can set certain limits, with the only signage requirements being
A designated speed established under this subsection is effective when
appropriate signs giving notice of the designated speed are posted on
the section of interstate highway where the designated speed is
imposed
and
A designated speed established under this subsection is effective when
appropriate signs giving notice of the designated speed are posted on
the portion of highway where the designated speed is imposed
which tells you the sign is somewhere on that section. Other authorities can impose speed limits, with the similar requirement (§5e) that
A designated speed established under this subsection is effective when
appropriate signs giving notice of the designated speed are posted on
the portion of the highway where the designated speed is imposed.
There is also a possibility of non-statutorily regulating speed on ocean shores, with the signage requirement that
A designated speed established under this subsection is effective when
posted upon appropriate fixed or variable signs on the portion of
ocean shore where the designated speed is imposed
A more precise variant is that
A road authority regulating the speed of vehicles under this
subsection shall post and maintain signs at all park entrances to give
notice of any designated speed
Those construction-related speed reductions have a requirement that
A sign giving notice of the temporary designated speed must be posted
at each end of the portion of highway where the temporary designated speed is imposed and at such other places on the highway as may be
necessary to inform the public
Emergency speed limits can also be imposed:
A speed established under this subsection is effective when
appropriate signs giving notice thereof are posted upon the highway
or portion of highway where the emergency speed is imposed.
Per §10c for residential areas with lower limits,
The road authority shall post a sign giving notice of the designated
speed at each end of the portion of highway where the designated speed
is imposed and at such other places on the highway as may be necessary
to inform the public
likewise under §11c
The city shall post a sign giving notice of the designated speed at
each end of the portion of highway where the designated speed is
imposed and at such other places on the highway as may be necessary to
inform the public
Speed limits that are established statutorily do not require signs. Exceptional limits do: the authority must designate a section of road to have such-and-such speed limit, and in order to be effective, they must also post a sign on that portion of the road. Suppose that the authority designates a reduced speed limit on Highway 10 between mileposts 12 and 17, but the signs are located 1/2 mile into that zone. Then the question is whether the reduced speed limit is effective for the entire "designated" distance despite the disparity between the zone-location and the actual sign position. As far as I know, this possibility has not been tested in court – road authorities seem to do a good job of matching signage with speed zone designations. The courts would indubitably interpret the boundary to be exactly at the sign.
Your behavioral interpretation of the law is correct, and given inviolable laws of physics (in the absence of infinite acceleration / deceleration technology), the law entails that (1) you must drive slower than the speed limit for some period of time immediately before entering the section with a lower designated limit and (2) if you are driving exactly at the speed limit, you may not drive at the new speed limit exactly at the instant that you cross out of the reduced-speed zone.
A propos the "which part of the car" question asked elsewhere, again, with current technology, the parts of the car are all going the same speed, so a violation would be if any part of the car is going too fast.