It has nothing to do with HTTPS. Cache is only controlled by the Expires/Cache-Control HTTP headers, which work the same regardless of whether the connection is encrypted or not. Most likely your production server is enforcing different cache headers than your development box.
Having said that, you should also employ server-side caching for such an expensive operation. Perhaps have the data be refreshed periodically by a cron-job or such and save them on the server for fast retrieval. Any page that requires 90 seconds of work to be displayed needs to be rethought.