I think everyone is different... I adjusted immeditately to clipless when I first used them (last october) and I was riding off road with them. I've never falled off due to them or anything like that. They feel completely natural to be honest and I can't imagine riding without them.
I always do this... unclip my dominate leg first (right leg), well before I plan on stopping so I can plant with that one, then unclip the left side. I also adjusted the tension on my pedals to my liking so they hold tight, but not so tight that I have to dislocate my knee to get out.
Only once did I crash off road going downhill at about 18mph and could have saved myself from being launched 10 feet through the air if I wasn't clipped in (couldn't get out fast enough to get off the bike when my front wheel instantly became stuck between two pieces of broken concrete.. crashes happen too quickly)...
I used mtb clipless pedals on my road bike and also mtb shoes (recessed cleat) so you can walk in them and not slide around.
As for being overly cautious, well, I think that's something you'll get over once you're more comfortable with them.