Q.lime tree or is it a mandarin?
I have what I thought was a lime tree. I picked a few a couple of months ago and used as limes. However, I have neglected them since, and the fruit has turned yellow. They are now segmented and taste like mandarins. Do you think the tree was mislabeled?

It could have been mislabeled, or (more likely) it could simply be refusing to obey the grower's instructions. Citrus freely pollinate each other, and all the citrus we use today are hybrids of hybrids.
Maybe you've lucked out - use the immature fruits as limes, and the mature ones as mandarins.