Just about every SDS in existence includes instructions to flush the eyes with water for "at least" 15 minutes if the material gets into one's eyes. The origin of the "15-minute rule" is not clear. In a few rare cases, such as splash involving hydrofluoric acid, it may unacceptably delay first aid treatment, and in cases involving bases, a longer time may be required (bases are very difficult to rinse out of eye tissues). And some experts suggest even 15 minutes is not sufficient in most cases. In any event, should you get (or suspect you got) a chemical in your eye, be sure to flush it with water for the time recommended on the SDS or label and contact your doctor or emergency room to see if further treatment is needed.
If you were wearing contact lenses at the time of the incident, proper use of your eye wash should have washed them away, but have someone examine your eyes to verify that they were removed. NIOSH has a "Current Intelligence Bulletin 59" titled "Contact Lens Use In a Chemical Environment" that addresses best practices for this formerly controversial topic.
When flushing the eyes, do your best to keep them open, and be sure to occasionally lift the upper and lower eyelids to ensure complete flushing.
As noted above, the use of a tempering unit (thermostatic mixing valve) to deliver tepid water is generally recommended. Imagine trying to flush your eyes with the water that comes out of the cold water faucet in wintertime. Not only is it unbearable, but the coldness of the water may also cause the victim to end the flushing before it has been fully effective!
Finally, when selecting eye protection, be sure to wear the kind that is most appropriate. Chemical splash goggles offer the best protection against impact and liquid splashes.