I'm not 100% sure the maps are fake, but Tumlinson found them and he was an avid rock carver. His carvings look similar to those on the Peralta stone maps. Half his family believes he carved them himself. Experts have said that the maps look to be carved with modern rotary tools. The heart symbol was not known, or very rare in Mexico 150+ years ago.
All of those things lead me to believe they are fake.
The maps are the type of "post road map" that was used by Mexicans at the time. The smaller symbols on the actual map part (cross inside brackets, circle with a dot in the center, Omega sign, etc.) do seem to be symbols used on Spanish/Mexican mine maps, and are used correctly and tell a story of how to get to the mine (at least if Charles Kenworthy is to be believed). Michael Bilbrey found two stone crosses which match the stone maps well (though these are possibly forgeries as well). Half of Tumlinson's family believed he thought they were real maps which would lead to treasure. There isn't much evidence that he ever tried to sell the maps, and he kept them secret. The motive for making fake maps would likely be to scam someone with them, and it doesn't appear that he tried that.
These things lead me to think the stone maps may be real. So you can see why I'm undecided.
The other possibility is that Tumlinson found the stone maps and carved more onto them. It does appear that some markings were done at a different time than others, judging by the wear and the depth and qualities of the carvings.
Or he may have had some other maps and consolidated them into one map which he carved on the stones, making them "real" but also created by Tumlinson.
But my overall impression of them is that they are probably not genuine and there are other maps which have fewer credibility issues. So I choose to focus on those instead.