I learned to build Self irrigation bucket from here and moved all my <1 year old trees to those bucket less than 2 month ago. They grow like crazy and I was very happy.

Until yesterday, I took a look at the lower bucket to check water level and found lots of roots come out from the bottom of the higher bucket! What should I do? Cut off these long roots? Or just leave them there sticking in the water?

Thank you for advice!

Shouldn't hurt them to be pruned back in the fall. But as long as it is really growing fast and leaves not yellowish your good

It is a good thing .That is what happens , just leave them alone .
I leave them alone until potting up to next size SIP.

Not much you can really do about it.  I tried adding weed fabric to the bottom of the SIP before adding soil and that helped a little bit, but they will still find a way out.  As Kerry and Richie mentioned, simply wait until they're dormant before messing with them.  I would pull out the entire root ball this winter, then cut about 1/4 of the bottom off, trim the sides, then backfill the SIP with fresh soil, then place the root ball back in the pot.  If the tree was root bound, cut away 1/3 of the size of the root ball.  Make sure you prune the top growth so it balances out with the root ball.

Here is an example of a root bound SIP I root pruned last winter.  Although a machete did the job, I went ahead a bought a reciprocating saw (which I can't wait to try out).

Thanks so much to all. I knew I can count on you guys and find answers here!