Yes, what type of server you have does matter. Your web hosts will know.

It's also extremely unlikely that adding a DirectoryIndex entry is going to resolve this for you. That would only be of benefit if you had a corrupt index.html file in your admin folder, when the suggested addition would cause the index.php to be executed instead. However, as Zen Cart doesn't have an index.html file in that folder, it shouldn't have any effect.

What advice or information did your web hosts give?