Missed a few, or some offsets grew in.

My experience with tulips is that they use so much strength up that they seldom rebloom, or rebloom weakly.
I believe, in order to get them to make a good display, here, the plants have the flowers removed and discarded so they build up strength for one display. Certainly no expert. Did buy them, even the species tulips, and they never went from year to year. Ours are from spent pots, set out, and once in a while one or two bloom again.

If you sliced a bulb, the remaining part could have been viable.

AFAIK, there's no way to know if you're getting real (heirloom I guess) tulips that bloom reliably every year, or some type of less reliable hybrid. You just have to wait and see what they do the next year if that's what you want to do.

It may just be that the info you were given is because winter locally doesn't provide the chill hours necessary for bud/bloom formation. I'm told and have read that that is the case here, I've never seen any in yards or in stores (except the potted, already growing bulbs) but I don't know where the cutoff point is usually made. I've never been interested enough to investigate if this means that the foliage comes back but no flowers ever form, or if they just die.

In central OH, "real" tulips are definitely reliable re-bloomers, long-lived bulbs - but that's a zone colder, I was in 5b very close to the Z6 line.

Tulips need a cold dormancy. If yours are happy with your winter they will return & rebloom. Don't dig them up unless they actually fail to return/rebloom. You probably left offsets, unfortunately these babies probably won't bloom this year... leave them in & see how they do. :-)

I get people from warmer zones constantly telling me that tulips don't return. Ignore them. Some will work for you, some may not. I know that in my (slightly colder) zone I have yet to have a tulip fail to rebloom.

People from Deep South warm climate zones are absolutely right. Tulips do not, as a rule, rebloom here. Our winters do not get cold enough for the bulbs to get adequate chill. We buy our bulbs in the fall, put them in the refrigerator for 8 to 10 weeks and plant them in January or February. If you leave them in the ground, it's likely that you will get green leaves from them for a few more years, but rarely a bloom, and if a bloom, it will be small and wimpy.
The OP, of course, is not from the Deep South, so it's entirely possible that if the right types of tulips are chosen, repeat blooms will be entirely possible. But based on the other posts, it would appear that it will be diminishing returns as time passes. So, if you want a full display, you'll need to replenish your plantings at least in part from year to year.

Thanks, Donna. I was wondering if they stay alive at all or just rot. I guess this is the reverse of people up north using Caladiums temporarily. It's been fascinating to learn how there is not a wider variety just because it's warmer here. So many favorites from up north can't live here, and so many of my new favorites are plants I'd never seen before moving south. Never much into tulips, but I miss lilacs!!

I grew up in Wichita and had lilac bushes outside my bedroom. They are beautiful and the fragrance is wonderful. I tried one years ago here that was suppsed to do well in the south, Miss Kim. It survived, but the blooms were extremely small and had very little fragrance. I eventually got rid of it. I content myself with butterfly bushes and chaste trees instead..

Obviously tulips grow and spread somewhere. That somewhere is the Mediterranean. They need coldish winters and dry summers. If they get the right climate, they will produce tiny bulbs that produce flowers eventually.

In my area (Zone 6 New England) tulips produce flowers a few years (progressively smaller each year) then die out.

In general, I believe the South has more flower options then the north.