I just noticed a few things with my cuttings; a few have roots coming out of the bottom of their plastic cups, and some of the ones that have leafed out have a few of their leaves that are brown and almost burnt looking.

Questions:

1. Roots coming out of the bottom, I assume that means one gallon time? Will they be ok without the humidity of being in a Tupperware bin at this point?

2. Why might some of the leaves be burnt looking? Temps only are in the low 70s, and there is no sunlight.

Are these in clear cups?  Roots coming out of the bottom does not mean 1 gallon.  You really need to see roots wrapping around the entire cup, almost root bound.  They will have less shock going into the 1 gallon pots and the soil will hold together better when transferring.
Each cuttings behaves differently.  Most will require humidity for a long time, while others may survive without it.  You can test their behavior by slowly exposing the cuttings to the room air and watching for leaf droop.  If they droop, then they need to go back in the humidity bin.

It's common for leaves to sprout, then turn brown and eventually fall off.  Another bud will emerge and you will get new leaves.  I don't know why this happens.  Last winter I raised over 130 cuttings and experienced a little bit of everything.  I lost maybe 10% total.

Yep, clear cups. Some have roots halfway around. I will wait a bit longer. I just don't know that I can fit a 1 gallon pot in my humidity bins... Hmmmm...

some roots will look strong, but most will be still brittle. meaning when moving the cutting from cup to 1 gal, there is chance that you will break lot of roots unless it's done really carefully. if the damage is big enough, it will delay or kill the cutting. you want as many roots are possible holding on to the soil mix and holding the shape of the current cup well, so you can more or less pull it out and plug it in to same soil mix in 1 gal. 

after being in 1 gal for awhile, the roots should harden enough bare rooting and moving to larger container shouldn't be much of an issue. 

this is one of the reason i use peat pot method. as long as i see few roots coming through the peat pot, i know they are ready to be moved to 1 gal. no need to wait for extensive growth since peat pot will hold the soil and the roots. but in winter.. i don't know if it make any difference since i keep the cutting in cups for months. 

This is the problem I noticed with the cup method. I start cuttings I plastic shoeboxes with moss and transfer to 4x4x9" tree pots. They are up potted from there to 3 gal containers in June-July. Almost no die back. If needed I use 2 clear Tupperware containers 1 right side up on the bottom w the other, upside down on the top as the lid. This year I'm going to try the root riot cubes and then jump to the tree pots.