What dialabrain said. Tags are a Finder extended attribute and will be stripped from tagged files when those files are placed on filesystems and Cloud services (e.g. Dropbox, Google Drive, etc.) that remove them.
Find Spotlight indexed files that have a red and purple tag on them.
tags:red and tags:purple
In English, and specifically, German-speaking countries, where Tag is defined as day in the locale dictionary, one must use the full Spotlight keyword directly, or separated as previously by a conjunction (e.g. and, or). In either of these examples, tag name strings may be defined/activated in Finder Preferences > Tags with an available color assigned to it.
kMDItemUserTags:red
Although Spotlight does not support regular expressions, or wildcards the following is sufficient to locate a file whose tag name string is Important:
kind:imp