In the case of noninstantaneous reheating with a period after inflation where the total energy density of the Universe redshifts as ${\rho }_{\mathrm{tot}}\sim a^{-n}$—with $n=3$, 4, 6 for matter, radiation, and kination eras—when the Hubble parameter is $H_{\inf }>H>H_{\mathrm{reh}}$ and $H_{\mathrm{osc}}>H_{\mathrm{reh}}$, we find that ${\overline{\rho }}_{\varphi ,\mathrm{kin}}$ remains unchanged, as it depends on the dynamics of the scalar field. On the other hand, instead of Eq. (15), we have ${\rho }_{\mathrm{tot},\mathrm{kin}}={\rho }_{\mathrm{kick}}^{\mathrm{tot}}{(a_{\mathrm{kick}}/a_{\mathrm{kin}})}^4(H_{\mathrm{reh}}/H_{\mathrm{kick}}{)}^{2(n-4)/n}$, where we used $H\propto a^{-n/2}$ for $H_{\inf }>H>H_{\mathrm{reh}}$. In this case, we find that the final ratio of the DM abundances depends on the reheating scale $H_{\mathrm{reh}}$ as, ${\mathrm{\Omega }}_{\text{fluct}}^0/{\mathrm{\Omega }}_{\mathrm{zero}}^0\propto {[\sqrt{2}{H}_{\inf }/(3H_{\mathrm{reh}})]}^{1-4/n}$ where the extra factor will modify ${\mathrm{\Omega }}_{\varphi }^{1/2}({\eta }_{\mathrm{kin}})$ in Eq. (10). The abundance of DM from axion fluctuation is suppressed when $n<4$, in particular for matter domination after inflation. On the contrary, the axion abundance is enhanced for a stiff era ($n>4$).