Usually when I divide sibs it's in the early spring when the leaves are just starting to show. I cut a pie shaped wedge out of the clump and transplant. I put a lot of old manure/compost into the missing wedge and fill the hole. Lot of compost in and around the transplants too. Sibs are heavy feeders especially in the spring. Really no trick to it just feed them and keep them moist until established which is pretty easy in the spring here.
Give them a good feeding with a fertilizer of some sort that's a bit on the acid side. Miracle grow for tomatoes or azalea's works great or if your like me with lots of horses some old manure in the early spring.
No lime! Sibs really resent it. Sets them right back. Nearly kills them. I even tested this on an old clump that I had a lot of this year. Died right back to the ground and had to regrow.

Feed them well early on and then again after bloom and you'll be rewarded this spring. Sibs can be a little fussy after transplant so as long as the plant looks good I doubt you did anything wrong.

I'm cool enough and moist enough where I can transplant any iris any time of the year as long as I give it enough time to establish before the cold sets in. I really like to give them a minimum of 8 weeks before the first killer frost.
Best if you move the iris you have now. More time before winter the better. Bearded iris like a little lime.

Nothing wrong with iris in a mixed bed. I sometimes have a hard time with it because I like the mixed, nearly chaotic cottage garden look but as long as the rhizomes are getting plenty of air and sun they do fine. Just have to keep tabs on them a bit.