Count resources in each category
You don't need to initialize the keys of results_map to 0. You can do it on the fly. Here is a generic example:

counts = {}
for value in values:
    if value in counts:
        counts[value] += 1
    else:
        counts[value] = 1

Even better, use collections.Counter instead. Generic example:

from collections import Counter

counts = Counter()
for value in values:
    counts[value] += 1

Refactor the method to check if app_name is in resource_name. Put APPS_MAP outside the functions so it can be accessed as a global variable.

def get_category(resource_name):
    for key, app_names in APPS_MAP.items()
        for app_name in app_names:
            if app_name in resource_name:
                return key
    return 'other'

Now you can rewrite the loop in count_resources_per_category() like this:

from collections import Counter

results_map = Counter()
for resource_name in resource_names:
    results_map[get_category(resource_name)] += 1
return results_map

It seems like determine_if_resource_count_issue() is checking to make sure only one field is non-zero. Here's a quick one-liner replacement. Put the print() statements outside this function.

def determine_if_resource_count_issue(results_map):
    return [v != 0 for v in results_map.values()].count(True) == 1

get_category() as implemented above is computationally expensive. Depending on your use case, you may want to consider using regex.
Don't pad your question with lorem ipsum lol.