Q: could adding a small amount of non honda antifreeze into overflow reservoir cause check engine light to appear a day later

Although it is not recommended to mix different antifreeze chemistries, that recommendation "usually" has more to do with avoiding negative effects (of mixing) on the service life of the coolant than any possibility for system damage. That is, mixing different coolants means you might have to change the coolant more frequently than the schedule set out by the manufacturer if you just simply use ONLY the manufacturer recommended coolant. As far as the check engine light coming on, in the wake of the "mixing", that is pure coincidence and is not causally related at all to what you added. The thing to do in your circumstance is to request a check engine light diagnostic and the responding certified mechanic will evaluate the Diagnostic Trouble Codes that have been set by the PCM and determine the root cause. Please let us know if you have any further concerns or needs.