Product review (4 stars): It feels better than the supplied connector
I bought this for the RO system. The push-in is 3/8" but my RO drain line is 1/4" so I inserted the 1/4" drain line into a short 3/8" tube and then inserted the end into the adapter. It works without any problem as long as it is not clogged. If you want to be safe, you could get an adapter.

The only real problem is that the branch on my drain pipe is 5/8" OD (regular 1/2" copper pipe) but this adapter has the 3/4" OD drain and the manual suggests that "it may be installed on a branch tailpiece receiving a 3/4" or 7/8" dishwasher drain hose" and the supplied connector couldn't be used. I ended up bought a dishwasher disposal connection from HD for less than $5. It feels better than the supplied connector. The wider end fits nicely with this adapter but I still need some Teflon tapes on the narrow end to connect it to my 5/8" drain pipe branch (since water would come from the wide end). After that all seem fine.