It’s the same way in Maine, although there are some who would like to change that. It doesn’t help that a woman was killed a few years ago by a hunter who thought she was a deer. Second time in 30 years...All these discussions on property boundaries and trespassing do not take into regional state laws.
I'm not a lawyer, though I do sleep with one at night, but I know the laws in Vermont were that I could generally hunt on other peoples land UNLESS it was POSTED whereas in Mississippi all land is "NO TRESPASSING" by default.
Getting back to the dogs running onto posted land; generally they are chasing a bear or raccoon which started on another property. That’s another thing which is different here than in other states; the game does not belong to the landowner.