ALTERNATE_WP_CRON constant is defined, WordPress will run WP-Cron on
init hook with priority
10 (the default).
Unfortunately, this means any code hooked to
init with priority
10 or higher will not be run before processing WP-Cron requests via the alternative WP-Cron method. This is a known issue with an open Trac ticket.
In the case of Subscriptions, where WP-Cron is the backbone for renewals, this can cause all sorts of issues. One such (very hard to diagnose) issue with PayPal subscriptions is addressed with PR 1733 and a similar, older issue is addressed in Action Scheduler with PR 24.