You cannot use the measurement protocol to trigger tags, since the measurement protocol is just that - a protocol. I.e. it is a description of how you have to format a http request if you expect the data to turn up in Google Analytics.
However there is a way to set up triggers, and I guess you are simply confused with the nomenclature - GTM has an API (an "advanced programming interface"). That is a set of conventions that can be used (in pretty much any language, including PHP) to create tags, triggers and variables via server-side calls.
The examples in the official documentation are for Java and Python, but there is an API client for PHP ( a library that provides functions to easily access Google services including GTM).
The basic idea is that you authorize against a Google account and then call a url that depends on the action you want to take (this is REST API, where the Urls represent resources that can be accessed via http), and then send your trigger configuration in the form of a JSON object in the body of the POST request.
What you cannot do (if that is your use case) is to trigger a tag (i.e. make a tag send data) in GTM via a server side call. GTM for the web is a javascript container that requires a client to run.