No the cities will share tech as long as the academy in the new cities are the correct level.

Eg your first city might have archery at level 10, but the other cities do not get it until they have an academy that can access archery ie lv4

Until then beside archery in the academy you would see

Lv 10 CT 0

Meaning you have researched level 10 but current city has that tech at 0

Infact in that city you could not even build archers in the correct level of barracks until the academy was 4 and any archers reinforced to that city would suddenly find they forgot all their training and where base range.