Is it just rinse with lots of cold water, see a doctor if they become irritated?

Yes.
Rinse, rinse, rinse again. Don’t hesitate to go get it looked at though.

I once had brake fluid in squirted in my eye from looking into a car master cylinder as someone squished the pedal, rinsed my eye out thoroughly and was fine but don’t take chances with your eyes.

Don’t bother with the doctor, just phone the eye clinic at your local hospital.

not the same stuff as I’m not sure what it actually is but the safety data sheet for other hydraulic fluid
http://www.defelsko.com/quality/AW_Hydraulic_Oil_MSDS.pdf

I got a little Shimano mineral oil in my eye recently when a brake I was bleeding suffered a sudden ejaculation.

I washed it thoroughly and was fine.

It may be closing the stable door after the horse has bolted, but having had a face full of dot 5 I always wear safety glasses when bleeding brakes etc.

For goodness sake don’t do anything until you’ve logged on to at least one cycling forum and asked strangers on the internet what they’d do. Under no circumstances should you seek actual medical advice, from professionals, and definitely don’t read the label on the fluid bottle either.

I’m delighted to tell you that having washed my eyes out thoroughly, looked at the bottle for advice, checked on a net forum and visited a pharmacist. My eyes still work and I’ve been for a ride.

I will be using goggles from now on tho.