When the 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.