Well the form of power projection was different as time went on.

One thing that must be said for any time period of Egyptian Levantine dominance is that the control could only be loose at best. It seems to have solidified into its most stable form under King Amenhotep III due to the lack of wars threatening the region at that time.

If we assume a date circa 1513/1512 BCE (that's the date given in the back of the New World Translation) then we are talking about the reign of King Ahmose.

If you are using that date for the Exodus (please specify) then there was no Egyptian Empire and that would more accurately match up with the Hebrews=Hyksos theory which has been pretty well disproved at this point.

If you meant the conquest of the Promised Land as outlined in Judges, then this would've been around the time of Egyptian King Thutmose III's conquest of the exact same region.

The dates in either case would be rather foggy, but it must be said that Thutmose III was the king responsible for installing rulers with Egyptian interests on the various Palestinian thrones.

According to Donald B Redford, the control that Egypt exercised in this time of the imperial expansion was rudimentary. Plenty of the kingdoms within region managed to put up enough resistance that they were merely reduced to a tributary state as opposed to being completely dominated. Even if Thutmose III did indeed install garrisons in places such as Ugarit (which he claims to have) these would've been overthrown by the time that his son began to rule.

I think that answers whether or not it was "fully a part of Egypt."

As to how badly they were treated, well the local land was used as fuel for the armies of Thutmose III. No longer would a campaigning king need to use a Nilotic base for his food supplies. Instead, select cities along the levantine coast were designated as harbors that could be used for supplying the army. That change in military strategy allowed for deeper and deeper campaigning into Asia.