My guess is that it's the Play Store app itself that does this (con.android.vending). That app is responsible for both updating itself regularly and installing/updating other apps.
One possible way: There is a daily job run in the Play Store called "daily hygiene" that performs various configured tasks based on device state and device targeting. It would not be difficult to add some code to install this app for MA users, then push it with the next Play Store update. I am very unpleasantly surprised that this app was installed from a policy perspective, however.
They don't have to add any code or push a Play Store update or wait for a daily cronjob. Listening for remote installation requests is a core feature of Google Play Services. It is not a mystery how this was done.
One possible way: There is a daily job run in the Play Store called "daily hygiene" that performs various configured tasks based on device state and device targeting. It would not be difficult to add some code to install this app for MA users, then push it with the next Play Store update. I am very unpleasantly surprised that this app was installed from a policy perspective, however.