Rebekah - I have seen many times throughout my time on Garden.org that folks have put mulch around/on top of rhizomes. It does not seem to affect them too much. Irises don't like water (as you know), so a fairly thin layer of mulch would help protect yet retain the summer waters that would cause rot issues. Though, I'm not 100% sure, I believe a mulch layer may increase the chances of rot.
I have a lot of varieties that are in/covered with mulch. I even buried some deeper down in mulch in fear of too much exposure. Except for noids (which have bloomed inside the mulch), all of my named varieties I have acquired came last year, and were planted then, so they have not yet bloomed.
Minus the fact that chickens have been ravaging towards these irises in mulch, most have grown well and increased too, but several varieties are very small in fan size. We'll see what they do.
In my experience, (and this garden is not the only place with mulch), irises will still willingly bloom as long as they don't get too much or too little water, or are crowded out by other plants also in the mulch. Your's look great so far, which is a great sign that you may be doing them a solid.
A YMCA near me had irises covered in mulch, and those irises bloom prolifically every year in the mulch. More with experience here than I can help you further, but I wish you good luck on your irises in mulch adventures!