My wife bought my first 4 figs from Willis 3 years ago for a Christmas present. Celestial, Black Jack, Italian and Texas Everbearing. Honestly, I don't know if they are true to type yet. They all tasted and looked the same last year, like Celeste. Although, the more I read about them the more I think some of what I bought are too similar to one another to see a difference yet, if at all ever. This year, I can tell that the Black jack is more compact just like I've read about, but the figs were not black last year. I've read that with age, fruit quality improves. We'll see.
Anyway, they came in as bare-root in Dec and I potted them up and they never broke dormancy. They replaced them free of charge (even though I didn't know what I was doing, and I think I screwed them up by overwatering them) and the next group rooted out and grew fine in March. Late June does seem late to ship bare-root, but their prices are reasonable. They must have kept them dormant in their coolers. Curious to see how you answer Martins question. Just keep all your paperwork. Can't remember if I had to ship the non-viable trees back.