The stats you see in the summary, are based on a calculation on IVs and Base Stats, that should update when leveling up.
While PKHeX does recalculate the stats in the summary screen (and it'll use the non-hacked base stats as part of the calculation), your summary stats should have been replaced by the hacked Base Stats of your hacked ROM hack upon level up.
If it doesn't, then who knows what the issue is.
An alternative, as I said earlier, is to use hax mode of PKHeX to write the wanted stats.