What just came out of my snake???

Okay, this is a weird question...but I am a first-time snake owner that hasn't seen all the things everyone on this board has - so hopefully you can help!

Anyway, I just got my male african house snake about 1 week ago (he's just under 4 months). I was playing with him this morning - all was usual. Then as I was putting him back in his container, I got the most brief glimpse of a small mass of tissue protruding from his cloaca. Just as quick as it appeared, it retracted and was gone.

I assume this is his penis, but is this normal? I found posts about "cloacal prolapse" online, but this doesn't seem to be the case, since it was just for a fleeting moment. Is this nothing to worry about?

Not having seen it, it is impossible to say what you saw...but the options are fairly limited. Regardless, as long as everything appears normal now, there is nothing to be concerned about.

If this is what I believe it is, it is normal and nothing to worry about.
Also, what you saw may, or may not, have been the hemipenes. IOW Sometimes it is the hemipenes, but it is not always the hemipenes, that you see when a snake does that action. Both males & females will evert some tissue, from cloaca, for various reasons (i.e. to musk, other defense move, prior to relieving itself, etc.).
This is my best educated guess since, of course, I/we have not seen what your snake did.
Also, a prolapse is rather unmistakable and certainly, by your description, does not sound like something that occurred with your snake (especially since nothing remained protruded).