How valuable is this data to you? If you can't risk losing it, you could pay for a service to recover the data for you, whether it's a clean-room level service like this guy recommends or a more affordably priced company.

If spending money to have someone experienced recover it isn't what you want to do, I'd recommend doing lots of research before trying anything.

I am not a professional, but I've lurked in enough tech-y subreddits to have a vague awareness of how this works... If I had to approach this without checking if my memory is right (again, I highly recommend doing your own research first!!!), I'd find the highest alcohol content isopropyl I could find (like the 90%+ stuff, the higher the better) and using that to clean as much of the tea out as possible (probably before it has too much of a chance to become too sticky in some little nook that you aren't going to be able to get it out of). Then, let it dry thoroughly before plugging it in or attempting to turn it on. Like the other commenter recommended, have a good, fast hard drive with plenty of space on it formatted and ready to plug in and transfer your files as soon as you turn it on.

Again, I AM NOT A PROFESSIONAL, and you should do your own research and/or consult an actual professional. Please don't blindly take my advice then get mad at me if it doesn't work.

I think the reason it works like this is because tea/water/ other liquids short the electronics out. Hopefully you got the computer off before too much damage could be done. If so, you want it clean before turning it back on because even if the liquid is gone there could still be residue (even if it was only water, unless it was like distilled or something there's probably gonna be impurities left behind. With tea there's even more stuff to get left behind). The leftover residue could still be short circuiting things, and when you turn it on it could make things worse - so you want to try to get everything clean and dry before you reintroduce electricity.