I'm using Magento or WooCommerce, does Codisto need a Cron job?

No, Codisto doesn't need a Cron job. The plugin is fully automated without the need to configure anything.

Advanced architecture means customer website browsing experience isn't affected regardless of the marketplace sync calculations and messages required.

I'm using Shopify or BigCommerce, do I need to be concerned about Cron jobs?

No, Cron jobs are server schedules sometimes set up on open source platforms like Magento or WooCommerce.  As a user of Shopify or BigCommerce you don't need to worry about anything like this - Codisto will 'just work'.