The initial treatment you have done following the fall of antibacterial surface cleaner is correct.
The next treatment depends on the strength of the chemical and severity of the injury
caused by it.
Since you have washed it immediately, severe injury is unlikely.
I advice you to consult your eye doctor for assessing the severity of injury and treatment accordingly which includes usage of antibiotic eye drops, steroid
eye drops, artificial eye drops. But this has to be done under medical supervision by a eye doctor as sometimes the chemical particles can be present in the eye inspite of washing and these need to be removed completely and treatment has to be tailored according to the severity of the disease.