Adventurers atlas positional awareness

I have recently started playing a 5.5e cartographer artificer and me and my DM have differing opinions on how the positional awareness for the adventurers atlas works.for me based off how it's written it states that as long as your on the same plane of existence you know their precise location. But my dms interpretation of the wording is that when you go to target them with the other map features you know the general location of them but you wouldn't be able to see if they were higher or lower than you and that the map would have a seemingly limited range. Which in my opinion defeats the purpose of having the magical map in the first place.

For those who don't know the feature

Lvl 3 Adventures Atlas.

Whenever you finish a Long Rest while holding Cartographer’s Tools, you can use that tool to create a set of magical maps by touching at least two creatures (one of whom can be yourself), up to a maximum number of creatures equal to 1 plus your Intelligence modifier (minimum of two creatures). Each target receives a magical map, which constantly updates to show the relative position of all the map holders but is illegible to all others. The maps last until you die or until you use this feature again, at which point any existing maps created by this feature immediately vanish.

While carrying the map, a target gains the following benefits.

Awareness. The target adds 1d4 to its Initiative rolls.

Positioning. The target knows the location of all other map holders that are on the same plane of existence as itself. When casting a spell or creating another effect that requires being able to see the effect’s target, a map holder can target another map holder regardless of sight or cover, so long as the other map holder is still within the effect’s range.

Your DM is inventing limitations to this feature that are not present in the actual rules. This is certainly within the purview of a DM to do, though in this case it seems pointlessly restrictive.

If your DM believes that the way they want it to work is how it actually works according to the rules, they're mistaken; there is nothing in the description of these features that specifies a limitation to the range of this effect or a restriction on vertical positioning.

Me and my dms discussion was how the feature works as written I am all for there being limitations if it is them just wanting to make the feature less powerful. But we were having a heated discussion about the feature as written and it felt like a never ending battle so I wanted to come here to get what other people believed how the feature functioned.

All I can say is that

The target knows the location of all other map holders that are on the same plane of existence as itself.

seems extremely straightforward to me. It does not say "the target knows the location of all other map holders within X feet", so there's no limitation on the range as written. It does not say "the target knows the horizontal position of all other map holders", so there's no limitation on knowing the map holders' vertical position. The feature doesn't work in those ways because it doesn't say it does.

It's not clear to me why your DM would believe that it does, but it may be useful to point out that the map is by definition magical and therefore not necessarily subject to any of the physical limitations that a mundane paper map would have.

Thank you