Some client reported that in some cases the client pay but is not clicking return to blesta website and then blesta is not recording the transaction. we have confirmed the behavior, and we are working in a solution but it will be as plugin. normally blesta is not allowing gateway to add their crontab, so the only option is to make it as plugin. the idea is to fetch all the payment done via checkout and loop throw it, if the payment is not present in blesta the cron add it.
Stripe support web hooks, but is globally, so if you are using 3 website with stripe, the web hook will notify only one URL, and can lead to payment issue for the other website, we suggest using web hooks only if you are suing stripe only in one blesta installation.
anyway the two option will be provided and every user should select wish one to implement.