It sounds like you did everything right... may have just overtightened the assembly nut.
So, back to your original question, "How tight do you tighten up on the nut on the drain"?
My answer is that you tighten the nut slightly less than you tightened it last time. You don't need to SUPER crank on the nut...just get a good firm tightening of the nut and then let the silicone set the needed amount of time and you should be fine!
If by chance you find that the anti.-friction washer is the issue you could always make your own snug fitting anti.-friction washer out of firm cardboard or even a thin plastic plate (or similar slippery flat material), right? I've done it a couple times on lavatory drain anti.-friction washers...the supplied cardboard anti.-friction washers were just so loose fitting that they spit out the side of the drain assembly nut like happened to you here. I made a better, tighter fitting anti.-friction washer out of a plastic plate for one and a painter's bucket side for another. I have also made a number of cardboard anti.-friction washers when I couldn't believe that a manufacturer didn't supply one with their particular drain assembly!!
Anyway, hopefully you will be all set from here! If you need anything else just let us know.