The reduced transition probabilities $B(E2; 0^+_{g.s.}\rightarrow2_1^+,2^+_2)$ in $^{70}$Zn and the full $B(E2; 0^+_{g.s.}\rightarrow2^+)$ strength up to S$_n$=7.79 MeV in $^{68}$Ni have been determined at the LISE/GANIL facility using the Coulomb-excitation technique at intermediate beam energy on a $^{208}$Pb target. The $\gamma$ rays emitted in-flight were detected with an array of 46 BaF$_2$ crystals. The angles of the deflected nuclei were determined in order to disentangle and extract the Coulomb and nuclear contributions to the excitation of the 2$^+$ states. The measured $B(E2; 0^+_{g.s.}\rightarrow2_1^+)$ of 1432(124) e$^2$fm$^4$ for $^{70}$Zn falls in the lower part of the published values which clustered either around 1600 or above 2000 e$^2$fm$^4$, while the $B(E2; 0^+_{g.s.}\rightarrow2^+_2)$ of 53(7) e$^2$fm$^4$ agrees very well with the two published values. The relatively low $B(E2; 0^+_{g.s.}\rightarrow2_1^+)$ of 301(38) e$^2$fm$^4$ for $^{68}$Ni agrees with previous studies and confirms a local magicity at $Z=28, N=40$. Combining the results of the low-energy spectra of $^{68}$Ni and $^{70}$Zn and their shell-model interpretations, it is interesting to notice that four different shapes (spherical, oblate, prolate and triaxial) are present. Finally, a summed $E2$ strength of only about 150 e$^2$fm$^4$ has been found experimentally at high excitation energy, likely due to proton excitations across the $Z=28$ gap. The experimental distribution of this high-energy $E2$ excitation agrees with SM calculations, but its strength is about two times weaker.< Réduire