Those do look like eyes and, if so, it is planted too shallow. Looking at your 2nd pic though it looks like the planting area is slightly sunken--something you want to avoid with peonies because it encourages puddling over the eyes and they do not do well sitting in water at all. If I were you I'd remove the mulch and add soil to the top so that it's slightly mounded. Your eyes should end up an inch to an inch and a half below soil level which should be perfect. As for mulch, if you decide to put it back on make sure that it isn't touching any of the stems and that you push it back so that it's not touching any of the new growth in the spring. I mulch as well, live in a very arid region, but have lost some to mold caused by the mulch.

Have never heard of Heart Strong, will have to look it up! And we need to see pics here when it blooms next spring!

There is a more active peony forum on garden.org, also free. Join me and a lot more there if you'd like! http://garden.org/users/join/LizinElizabeth/